%% Papers Published
@article{fds375960,
Author = {Barthel, T and Miao, Q},
Title = {Absence of barren plateaus and scaling of gradients in the
energy optimization of isometric tensor network
states},
Journal = {arXiv:2304.00161},
Year = {2023},
Month = {March},
url = {https://doi.org/10.48550/arXiv.2304.00161},
Abstract = {Vanishing gradients can pose substantial obstacles for
high-dimensional optimization problems. Here we consider
energy minimization problems for quantum many-body systems
with extensive Hamiltonians, which can be studied on
classical computers or in the form of variational quantum
eigensolvers on quantum computers. Barren plateaus
correspond to scenarios where the average amplitude of the
energy gradient decreases exponentially with increasing
system size. This occurs, for example, for quantum neural
networks and for brickwall quantum circuits when the depth
increases polynomially in the system size. Here we prove
that the variational optimization problems for matrix
product states, tree tensor networks, and the multiscale
entanglement renormalization ansatz are free of barren
plateaus. The derived scaling properties for the gradient
variance provide an analytical guarantee for the
trainability of randomly initialized tensor network states
(TNS) and motivate certain initialization schemes. In a
suitable representation, unitary tensors that parametrize
the TNS are sampled according to the uniform Haar measure.
We employ a Riemannian formulation of the gradient based
optimizations which simplifies the analytical
evaluation.},
Doi = {10.48550/arXiv.2304.00161},
Key = {fds375960}
}
@article{fds302498,
Author = {Cai, Z and Barthel, T},
Title = {Algebraic versus exponential decoherence in dissipative
many-particle systems},
Journal = {Physical Review Letters},
Volume = {111},
Number = {15},
Pages = {150403},
Year = {2013},
Month = {October},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.111.150403},
Abstract = {The interplay between dissipation and internal interactions
in quantum many-body systems gives rise to a wealth of novel
phenomena. Here we investigate spin-1/2 chains with uniform
local couplings to a Markovian environment using the
time-dependent density matrix renormalization group. For the
open XXZ model, we discover that the decoherence time
diverges in the thermodynamic limit. The coherence decay is
then algebraic instead of exponential. This is due to a
vanishing gap in the spectrum of the corresponding Liouville
superoperator and can be explained on the basis of a
perturbative treatment. In contrast, decoherence in the open
transverse-field Ising model is found to be always
exponential. In this case, the internal interactions can
both facilitate and impede the environment-induced
decoherence. © 2013 American Physical Society.},
Doi = {10.1103/PhysRevLett.111.150403},
Key = {fds302498}
}
@article{fds318404,
Author = {Mölter, J and Barthel, T and Schollwöck, U and Alba,
V},
Title = {Bound states and entanglement in the excited states of
quantum spin chains},
Journal = {Journal of Statistical Mechanics: Theory and
Experiment},
Volume = {2014},
Number = {10},
Pages = {P10029-P10029},
Publisher = {IOP Publishing},
Year = {2014},
Month = {October},
url = {http://dx.doi.org/10.1088/1742-5468/2014/10/P10029},
Abstract = {We investigate the entanglement properties of the excited
states of the spin-1/2 Heisenberg (XXX) chain with isotropic
antiferromagnetic interactions, by exploiting the Bethe
ansatz solution of the model. We consider eigenstates
obtained from both real and complex solutions ('strings') of
the Bethe equations. Physically, the former are states of
interacting magnons, whereas the latter contain bound states
of groups of particles. We first focus on the situation with
few particles in the chain. Using exact results and
semiclassical arguments, we derive an upper bound SMAX for
the entanglement entropy. This exhibits an intermediate
behaviour between logarithmic and extensive, and it is
saturated for highly-entangled states. As a function of the
eigenstate energy, the entanglement entropy is organized in
bands. Their number depends on the number of blocks of
contiguous Bethe.Takahashi quantum numbers. In the presence
of bound states a significant reduction in the entanglement
entropy occurs, reflecting that a group of bound particles
behaves effectively as a single particle. Interestingly, the
associated entanglement spectrum shows edge-related levels.
At a finite particle density, the semiclassical bound SMAX
becomes inaccurate. For highly-entangled states SA ∝ Lc,
with Lc the chord length, signalling the crossover to
extensive entanglement. Finally, we consider eigenstates
containing a single pair of bound particles. No significant
entanglement reduction occurs, in contrast with the
fewparticle case.},
Doi = {10.1088/1742-5468/2014/10/P10029},
Key = {fds318404}
}
@article{fds302487,
Author = {Barthel, T and Pineda, C and Eisert, J},
Title = {Contraction of fermionic operator circuits and the
simulation of strongly correlated fermions},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {80},
Number = {4},
Publisher = {American Physical Society (APS)},
Year = {2009},
Month = {October},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.80.042333},
Abstract = {A fermionic operator circuit is a product of fermionic
operators of usually different and partially overlapping
support. Further elements of fermionic operator circuits
(FOCs) are partial traces and partial projections. The
presented framework allows for the introduction of fermionic
versions of known qudit operator circuits (QUOC), important
for the simulation of strongly correlated d -dimensional
systems: the multiscale entanglement renormalization
ansätze (MERA), tree tensor networks (TTN), projected
entangled pair states (PEPS), or their infinite-size
versions (iPEPS etc.). After the definition of a FOC, we
present a method to contract it with the same computation
and memory requirements as a corresponding QUOC, for which
all fermionic operators are replaced by qudit operators of
identical dimension. A given scheme for contracting the QUOC
relates to an analogous scheme for the corresponding
fermionic circuit, where additional marginal computational
costs arise only from reordering of modes for operators
occurring in intermediate stages of the contraction. Our
result hence generalizes efficient schemes for the
simulation of d -dimensional spin systems, as MERA, TTN, or
PEPS to the fermionic case. © 2009 The American Physical
Society.},
Doi = {10.1103/PhysRevA.80.042333},
Key = {fds302487}
}
@article{fds375961,
Author = {Miao, Q and Barthel, T},
Title = {Convergence and quantum advantage of Trotterized MERA for
strongly-correlated systems},
Journal = {arXiv:2303.08910},
Year = {2023},
Month = {March},
url = {https://doi.org/10.48550/arXiv.2303.08910},
Abstract = {Strongly-correlated quantum many-body systems are difficult
to study and simulate classically. We recently proposed a
variational quantum eigensolver (VQE) based on the
multiscale entanglement renormalization ansatz (MERA) with
tensors constrained to certain Trotter circuits. Here, we
extend the theoretical analysis, testing different
initialization and convergence schemes, determining the
scaling of computation costs for various critical spin
models, and establishing a quantum advantage. For the
Trotter circuits being composed of single-qubit and
two-qubit rotations, it is experimentally advantageous to
have small rotation angles. We find that the average angle
amplitude can be reduced substantially with negligible
effect on the energy accuracy. Benchmark simulations show
that choosing TMERA tensors as brick-wall circuits or
parallel random-pair circuits yields very similar energy
accuracies.},
Doi = {10.48550/arXiv.2303.08910},
Key = {fds375961}
}
@article{fds376286,
Author = {Zhang, Y and Barthel, T},
Title = {Criteria for Davies irreducibility of Markovian quantum
dynamics},
Journal = {Journal of Physics A: Mathematical and Theoretical},
Volume = {57},
Number = {11},
Year = {2024},
Month = {March},
url = {http://dx.doi.org/10.1088/1751-8121/ad2a1e},
Abstract = {The dynamics of Markovian open quantum systems are described
by Lindblad master equations, generating a quantum dynamical
semigroup. An important concept for such systems is (Davies)
irreducibility, i.e. the question whether there exist
non-trivial invariant subspaces. Steady states of
irreducible systems are unique and faithful, i.e. they have
full rank. In the 1970s, Frigerio showed that a system is
irreducible if the Lindblad operators span a self-adjoint
set with trivial commutant. We discuss a more general and
powerful algebraic criterion, showing that a system is
irreducible if and only if the multiplicative algebra
generated by the Lindblad operators La and the operator i H
+ ∑ a L a † L a , involving the Hamiltonian H, is the
entire operator space. Examples for two-level systems, show
that a change of Hamiltonian terms as well as the addition
or removal of dissipators can render a reducible system
irreducible and vice versa. Examples for many-body systems
show that a large class of spin chains can be rendered
irreducible by dissipators on just one or two sites.
Additionally, we discuss the decisive differences between
(Davies) reducibility and Evans reducibility for quantum
channels and dynamical semigroups which has lead to some
confusion in the recent physics literature, especially, in
the context of boundary-driven systems. We give a criterion
for quantum reducibility in terms of associated classical
Markov processes and, lastly, discuss the relation of the
main result to the stabilization of pure states and argue
that systems with local Lindblad operators cannot stabilize
pure Fermi-sea states.},
Doi = {10.1088/1751-8121/ad2a1e},
Key = {fds376286}
}
@article{fds375957,
Author = {Zhang, Y and Barthel, T},
Title = {Criteria for Davies irreducibility of Markovian quantum
dynamics},
Journal = {arXiv:2310.17641},
Year = {2023},
Month = {October},
url = {https://doi.org/10.48550/arXiv.2310.17641},
Abstract = {The dynamics of Markovian open quantum systems are described
by Lindblad master equations, generating a quantum dynamical
semigroup. An important concept for such systems is (Davies)
irreducibility, i.e., the question whether there exist
non-trivial invariant subspaces. Steady states of
irreducible systems are unique and faithful, i.e., they have
full rank. In the 1970s, Frigerio showed that a system is
irreducible if the Lindblad operators span a self-adjoint
set with trivial commutant. We discuss a more general and
powerful algebraic criterion, showing that a system is
irreducible if and only if the multiplicative algebra
generated by the Lindblad operators $L_a$ and the operator
$iH+\sum_a L^+_aL_a$, involving the Hamiltonian $H$, is the
entire operator space. Examples for two-level systems, show
that a change of Hamiltonian terms as well as the addition
or removal of dissipators can render a reducible system
irreducible and vice versa. Examples for many-body systems
show that a large class of spin chains can be rendered
irreducible by dissipators on just one or two sites.
Additionally, we discuss the decisive differences between
(Davies) reducibility and Evans reducibility for quantum
channels and dynamical semigroups which has lead to some
confusion in the recent physics literature, especially, in
the context of boundary-driven systems. We give a criterion
for quantum reducibility in terms of associated classical
Markov processes and, lastly, discuss the relation of the
main result to the stabilization of pure states and argue
that systems with local Lindblad operators cannot stabilize
pure Fermi-sea states.},
Doi = {10.48550/arXiv.2310.17641},
Key = {fds375957}
}
@article{fds367260,
Author = {Zhang, Y and Barthel, T},
Title = {Criticality and Phase Classification for Quadratic Open
Quantum Many-Body Systems},
Journal = {Physical Review Letters},
Volume = {129},
Number = {12},
Pages = {120401},
Year = {2022},
Month = {September},
url = {http://dx.doi.org/10.1103/PhysRevLett.129.120401},
Abstract = {We study the steady states of translation-invariant open
quantum many-body systems governed by Lindblad master
equations, where the Hamiltonian is quadratic in the ladder
operators, and the Lindblad operators are either linear or
quadratic and Hermitian. These systems are called quasifree
and quadratic, respectively. We find that steady states of
one-dimensional systems with finite-range interactions
necessarily have exponentially decaying Green's functions.
For the quasifree case without quadratic Lindblad operators,
we show that fermionic systems with finite-range
interactions are noncritical for any number of spatial
dimensions and provide bounds on the correlation lengths.
Quasifree bosonic systems can be critical in D>1 dimensions.
Last, we address the question of phase transitions in
quadratic systems and find that, without symmetry
constraints beyond invariance under single-particle basis
and particle-hole transformations, all gapped Liouvillians
belong to the same phase.},
Doi = {10.1103/PhysRevLett.129.120401},
Key = {fds367260}
}
@article{fds302492,
Author = {Barthel, T and Schollwöck, U},
Title = {Dephasing and the steady state in quantum many-particle
systems},
Journal = {Physical Review Letters},
Volume = {100},
Number = {10},
Pages = {100601},
Year = {2008},
Month = {March},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.100.100601},
Abstract = {We discuss relaxation in bosonic and fermionic many-particle
systems. For integrable systems, time evolution can cause a
dephasing effect, leading for finite subsystems to steady
states. We explicitly derive those steady subsystem states
and devise sufficient prerequisites for the dephasing to
occur. We also find simple scenarios, in which dephasing is
ineffective and discuss the dependence on dimensionality and
criticality. It follows further that, after a quench of
system parameters, entanglement entropy will become
extensive. This provides a way of creating strong
entanglement in a controlled fashion. © 2008 The American
Physical Society.},
Doi = {10.1103/PhysRevLett.100.100601},
Key = {fds302492}
}
@article{fds302493,
Author = {Kliesch, M and Barthel, T and Gogolin, C and Kastoryano, M and Eisert,
J},
Title = {Dissipative quantum Church-Turing theorem},
Journal = {Physical Review Letters},
Volume = {107},
Number = {12},
Pages = {120501},
Year = {2011},
Month = {September},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.107.120501},
Abstract = {We show that the time evolution of an open quantum system,
described by a possibly time dependent Liouvillian, can be
simulated by a unitary quantum circuit of a size scaling
polynomially in the simulation time and the size of the
system. An immediate consequence is that dissipative quantum
computing is no more powerful than the unitary circuit
model. Our result can be seen as a dissipative Church-Turing
theorem, since it implies that under natural assumptions,
such as weak coupling to an environment, the dynamics of an
open quantum system can be simulated efficiently on a
quantum computer. Formally, we introduce a Trotter
decomposition for Liouvillian dynamics and give explicit
error bounds. This constitutes a practical tool for
numerical simulations, e.g., using matrix-product operators.
We also demonstrate that most quantum states cannot be
prepared efficiently. © 2011 American Physical
Society.},
Doi = {10.1103/PhysRevLett.107.120501},
Key = {fds302493}
}
@article{fds302499,
Author = {Halimeh, JC and Wöllert, A and McCulloch, I and Schollwöck, U and Barthel, T},
Title = {Domain-wall melting in ultracold-boson systems with hole and
spin-flip defects},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {89},
Number = {6},
Publisher = {American Physical Society (APS)},
Year = {2014},
Month = {June},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.89.063603},
Abstract = {Quantum magnetism is a fundamental phenomenon of nature. As
of late, it has garnered a lot of interest because
experiments with ultracold atomic gases in optical lattices
could be used as a simulator for phenomena of magnetic
systems. A paradigmatic example is the time evolution of a
domain-wall state of a spin-1/2 Heisenberg chain, the
so-called domain-wall melting. The model can be implemented
by having two species of bosonic atoms with unity filling
and strong on-site repulsion U in an optical lattice. In
this paper, we study the domain-wall melting in such a setup
on the basis of the time-dependent density matrix
renormalization group (tDMRG). We are particularly
interested in the effects of defects that originate from an
imperfect preparation of the initial state. Typical defects
are holes (empty sites) and flipped spins. We show that the
dominating effects of holes on observables like the
spatially resolved magnetization can be taken account of by
a linear combination of spatially shifted observables from
the clean case. For sufficiently large U, further effects
due to holes become negligible. In contrast, the effects of
spin flips are more severe as their dynamics occur on the
same time scale as that of the domain-wall melting itself.
It is hence advisable to avoid preparation schemes that are
based on spin flips. © 2014 American Physical
Society.},
Doi = {10.1103/PhysRevA.89.063603},
Key = {fds302499}
}
@article{fds376287,
Author = {Zhang, Y and Barthel, T},
Title = {Driven-dissipative Bose-Einstein condensation and the upper
critical dimension},
Journal = {Physical Review A},
Volume = {109},
Number = {2},
Year = {2024},
Month = {February},
url = {http://dx.doi.org/10.1103/PhysRevA.109.L021301},
Abstract = {Driving and dissipation can stabilize Bose-Einstein
condensates. Using Keldysh field theory, we analyze this
phenomenon for Markovian systems that can comprise on-site
two-particle driving, on-site single-particle and
two-particle loss, as well as edge-correlated pumping. Above
the upper critical dimension, mean-field theory shows that
pumping and two-particle driving induce condensation right
at the boundary between the stable and unstable regions of
the noninteracting theory. With nonzero two-particle
driving, the condensate is gapped. This picture is
consistent with the recent observation that, without
symmetry constraints beyond invariance under single-particle
basis transformations, all gapped quadratic bosonic
Liouvillians belong to the same phase. For systems below the
upper critical dimension, the edge-correlated pumping
penalizes high-momentum fluctuations, rendering the theory
renormalizable. We perform the one-loop renormalization
group analysis, finding a condensation transition inside the
unstable region of the noninteracting theory. Interestingly,
its critical behavior is determined by a Wilson-Fisher-like
fixed point with universal correlation-length exponent
ν=0.6 in three dimensions.},
Doi = {10.1103/PhysRevA.109.L021301},
Key = {fds376287}
}
@article{fds375956,
Author = {Zhang, Y and Barthel, T},
Title = {Driven-dissipative Bose-Einstein condensation and the upper
critical dimension},
Journal = {arXiv:2311.13561},
Year = {2023},
Month = {November},
url = {https://doi.org/10.48550/arXiv.2311.13561},
Abstract = {Driving and dissipation can stabilize Bose-Einstein
condensates. Using Keldysh field theory, we analyze this
phenomenon for Markovian systems that can comprise on-site
two-particle driving, on-site single-particle and
two-particle loss, as well as edge-correlated pumping. Above
the upper critical dimension, mean-field theory shows that
pumping and two-particle driving induce condensation right
at the boundary between the stable and unstable regions of
the non-interacting theory. With nonzero two-particle
driving, the condensate is gapped. This picture is
consistent with the recent observation that, without
symmetry constraints beyond invariance under single-particle
basis transformations, all gapped quadratic bosonic
Liouvillians belong to the same phase. For systems below the
upper critical dimension, the edge-correlated pumping
penalizes high-momentum fluctuations, rendering the theory
renormalizable. We perform the one-loop renormalization
group analysis, finding a condensation transition inside the
unstable region of the non-interacting theory.
Interestingly, its critical behavior is determined by a
Wilson-Fisher-like fixed point with universal
correlation-length exponent nu=0.6 in three
dimensions.},
Doi = {10.48550/arXiv.2311.13561},
Key = {fds375956}
}
@article{fds362482,
Author = {Miao, Q and Barthel, T},
Title = {Eigenstate entanglement scaling for critical interacting
spin chains},
Journal = {Quantum},
Volume = {6},
Pages = {642},
Year = {2022},
Month = {January},
url = {http://dx.doi.org/10.22331/Q-2022-02-02-642},
Abstract = {With increasing subsystem size and energy, bipartite
entanglement entropies of energy eigenstates cross over from
the groundstate scaling to a volume law. In previous work,
we pointed out that, when strong or weak eigenstate
thermalization (ETH) applies, the entanglement entropies of
all or, respectively, almost all eigenstates follow a single
crossover function. The crossover functions are determined
by the subsystem entropy of thermal states and assume
universal scaling forms in quantum-critical regimes. This
was demonstrated by field-theoretical arguments and the
analysis of large systems of non-interacting fermions and
bosons. Here, we substantiate such scaling properties for
integrable and non-integrable interacting spin-1/2 chains at
criticality using exact diagonalization. In particular, we
analyze XXZ and transverse-field Ising models with and
without next-nearest-neighbor interactions. Indeed, the
crossover of thermal subsystem entropies can be described by
a universal scaling function following from conformal field
theory. Furthermore, we analyze the validity of ETH for
entanglement in these models. Even for the relatively small
system sizes that can be simulated, the distributions of
eigenstate entanglement entropies are sharply peaked around
the subsystem entropies of the corresponding thermal
ensembles.},
Doi = {10.22331/Q-2022-02-02-642},
Key = {fds362482}
}
@article{fds354044,
Author = {Miao, Q and Barthel, T},
Title = {Eigenstate entanglement scaling for critical interacting
spin chains},
Journal = {arXiv:2010.07265},
Year = {2020},
Month = {October},
Abstract = {With increasing subsystem size and energy, bipartite
entanglement entropies of energy eigenstates cross over from
the groundstate scaling to a volume law. In previous work,
we pointed out that, when strong or weak eigenstate
thermalization (ETH) applies, the entanglement of all or,
respectively, almost all eigenstates follow universal
scaling functions which are determined by the subsystem
entropy of thermal states. This was demonstrated by
field-theoretical arguments and by analysis of large systems
of non-interacting fermions and bosons. Here, we further
substantiate such scaling properties for integrable and
non-integrable interacting spin-1/2 chains at criticality
using exact diagonalization. In particular, we analyze XXZ
and transverse-field Ising models with and without
next-nearest-neighbor interactions. We first confirm that
the crossover for subsystem entropies in thermal ensembles
can be described by a universal scaling function following
from conformal field theory. Then, we analyze the validity
of ETH for entanglement in these models. Even for the
relatively small system sizes that can be simulated, the
distributions of eigenstate entanglement entropies are
sharply peaked around the subsystem entropies of the
corresponding thermal ensembles.},
Key = {fds354044}
}
@article{fds360764,
Author = {Q. Miao and T. Barthel},
Title = {Eigenstate entanglement: Crossover from the ground state to
volume laws},
Journal = {Phys. Rev. Lett.},
Volume = {127},
Pages = {040603},
Year = {2021},
Month = {July},
url = {http://dx.doi.org/10.1103/PhysRevLett.127.040603},
Doi = {10.1103/PhysRevLett.127.040603},
Key = {fds360764}
}
@article{fds347982,
Author = {Miao, Q and Barthel, T},
Title = {Eigenstate Entanglement: Crossover from the Ground State to
Volume Laws},
Journal = {Physical Review Letters},
Volume = {127},
Number = {4},
Year = {2021},
Month = {July},
url = {http://arxiv.org/abs/1905.07760},
Abstract = {For the typical quantum many-body systems that obey the
eigenstate thermalization hypothesis (ETH), we argue that
the entanglement entropy of (almost) all energy eigenstates
is described by a single crossover function. The ETH implies
that the crossover functions can be deduced from subsystem
entropies of thermal ensembles and have universal
properties. These functions capture the full crossover from
the ground-state entanglement regime at low energies and
small subsystem size (area or log-area law) to the extensive
volume-law regime at high energies or large subsystem size.
For critical one-dimensional systems, a universal scaling
function follows from conformal field theory and can be
adapted for nonlinear dispersions. We use it to also deduce
the crossover scaling function for Fermi liquids in d>1
dimensions. The analytical results are complemented by
numerics for large noninteracting systems of fermions in
d≤3 dimensions and have also been confirmed for bosonic
systems and nonintegrable spin chains.},
Doi = {10.1103/PhysRevLett.127.040603},
Key = {fds347982}
}
@article{fds302485,
Author = {Zhou, HQ and Barthel, T and Fjærestad, JO and Schollwöck,
U},
Title = {Entanglement and boundary critical phenomena},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {74},
Number = {5},
Publisher = {American Physical Society (APS)},
Year = {2006},
Month = {November},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.74.050305},
Abstract = {We investigate boundary critical phenomena from a
quantum-information perspective. Bipartite entanglement in
the ground state of one-dimensional quantum systems is
quantified using the Rényi entropy Sα, which includes the
von Neumann entropy (α→1) and the single-copy
entanglement (α→) as special cases. We identify the
contribution of the boundaries to the Rényi entropy, and
show that there is an entanglement loss along boundary
renormalization group (RG) flows. This property, which is
intimately related to the Affleck-Ludwig g theorem, is a
consequence of majorization relations between the spectra of
the reduced density matrix along the boundary RG flows. We
also point out that the bulk contribution to the single-copy
entanglement is half of that to the von Neumann entropy,
whereas the boundary contribution is the same. © 2006 The
American Physical Society.},
Doi = {10.1103/PhysRevA.74.050305},
Key = {fds302485}
}
@article{fds302491,
Author = {Barthel, T and Dusuel, S and Vidal, J},
Title = {Entanglement entropy beyond the free case},
Journal = {Physical Review Letters},
Volume = {97},
Number = {22},
Pages = {220402},
Year = {2006},
Month = {January},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.97.220402},
Abstract = {We present a perturbative method to compute the ground state
entanglement entropy for interacting systems. We apply it to
a collective model of mutually interacting spins in a
magnetic field. At the quantum critical point, the
entanglement entropy scales logarithmically with the
subsystem size, the system size, and the anisotropy
parameter. We determine the corresponding scaling prefactors
and evaluate the leading finite-size correction to the
entropy. Our analytical predictions are in perfect agreement
with numerical results. © 2006 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.97.220402},
Key = {fds302491}
}
@article{fds302484,
Author = {Vidal, J and Dusuel, S and Barthel, T},
Title = {Entanglement entropy in collective models},
Journal = {Journal of Statistical Mechanics: Theory and
Experiment},
Volume = {2007},
Number = {1},
Pages = {P01015-P01015},
Publisher = {IOP Publishing},
Year = {2007},
Month = {January},
url = {http://dx.doi.org/10.1088/1742-5468/2007/01/P01015},
Abstract = {We discuss the behaviour of the entanglement entropy of the
ground state in various collective systems. Results for
general quadratic two-mode boson models are given, yielding
the relation between quantum phase transitions of the system
(signalled by a divergence of the entanglement entropy) and
the excitation energies. Such systems naturally arise when
expanding collective spin Hamiltonians at leading order via
the Holstein-Primakoff mapping. In a second step, we analyse
several such models (the Dicke model, the two-level
Bardeen-Cooper-Schrieffer model, the Lieb-Mattis model and
the Lipkin-Meshkov-Glick model) and investigate the
properties of the entanglement entropy over the whole
parameter range. We show that when the system contains
gapless excitations the entanglement entropy of the ground
state diverges with increasing system size. We derive and
classify the scaling behaviours that can be met. © IOP
Publishing Ltd.},
Doi = {10.1088/1742-5468/2007/01/P01015},
Key = {fds302484}
}
@article{fds302486,
Author = {Barthel, T and Chung, MC and Schollwöck, U},
Title = {Entanglement scaling in critical two-dimensional fermionic
and bosonic systems},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {74},
Number = {2},
Publisher = {American Physical Society (APS)},
Year = {2006},
Month = {September},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.74.022329},
Abstract = {We relate the reduced density matrices of quadratic
fermionic and bosonic models to their Green's function
matrices in a unified way and calculate the scaling of the
entanglement entropy of finite systems in an infinite
universe exactly. For critical fermionic two-dimensional
(2D) systems at T=0, two regimes of scaling are identified:
generically, we find a logarithmic correction to the area
law with a prefactor dependence on the chemical potential
that confirms earlier predictions based on the Widom
conjecture. If, however, the Fermi surface of the critical
system is zero-dimensional, then we find an area law with a
sublogarithmic correction. For a critical bosonic 2D array
of coupled oscillators at T=0, our results show that the
entanglement entropy follows the area law without
corrections. © 2006 The American Physical
Society.},
Doi = {10.1103/PhysRevA.74.022329},
Key = {fds302486}
}
@article{fds302483,
Author = {Kliesch, M and Barthel, T and Gogolin, C and Kastoryano, M and Eisert,
J},
Title = {Erratum: Dissipative quantum church-turing theorem (Physical
Review Letters (2011) 107 (120501))},
Journal = {Physical Review Letters},
Volume = {109},
Number = {11},
Publisher = {American Physical Society (APS)},
Year = {2012},
Month = {September},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.109.119904},
Doi = {10.1103/PhysRevLett.109.119904},
Key = {fds302483}
}
@article{fds318402,
Author = {Gori, L and Barthel, T and Kumar, A and Lucioni, E and Tanzi, L and Inguscio, M and Modugno, G and Giamarchi, T and D'Errico, C and Roux,
G},
Title = {Finite-temperature effects on interacting bosonic
one-dimensional systems in disordered lattices},
Journal = {Physical Review A},
Volume = {93},
Number = {3},
Publisher = {American Physical Society (APS)},
Year = {2016},
Month = {March},
url = {http://dx.doi.org/10.1103/PhysRevA.93.033650},
Abstract = {We analyze the finite-temperature effects on the phase
diagram describing the insulating properties of interacting
one-dimensional bosons in a quasiperiodic lattice. We
examine thermal effects by comparing experimental results to
exact diagonalization for small-sized systems and to
density-matrix renormalization group (DMRG) computations. At
weak interactions, we find short thermal correlation
lengths, indicating a substantial impact of temperature on
the system coherence. Conversely, at strong interactions,
the obtained thermal correlation lengths are significantly
larger than the localization length, and the quantum nature
of the T=0 Bose-glass phase is preserved up to a crossover
temperature that depends on the disorder strength.
Furthermore, in the absence of disorder, we show how
quasiexact finite-T DMRG computations, compared to
experimental results, can be employed to estimate the
temperature, which is not directly accessible in the
experiment.},
Doi = {10.1103/PhysRevA.93.033650},
Key = {fds318402}
}
@article{fds338335,
Author = {Barthel, T and Lu, J},
Title = {Fundamental Limitations for Measurements in Quantum
Many-Body Systems},
Journal = {Physical Review Letters},
Volume = {121},
Number = {8},
Pages = {080406},
Year = {2018},
Month = {August},
url = {http://dx.doi.org/10.1103/PhysRevLett.121.080406},
Abstract = {Dynamical measurement schemes are an important tool for the
investigation of quantum many-body systems, especially in
the age of quantum simulation. Here, we address the question
whether generic measurements can be implemented efficiently
if we have access to a certain set of experimentally
realizable measurements and can extend it through time
evolution. For the latter, two scenarios are considered: (a)
evolution according to unitary circuits and (b) evolution
due to Hamiltonians that we can control in a time-dependent
fashion. We find that the time needed to realize a certain
measurement to a predefined accuracy scales in general
exponentially with the system size - posing a fundamental
limitation. The argument is based on the construction of
μ-packings for manifolds of observables with identical
spectra and a comparison of their cardinalities to those of
μ-coverings for quantum circuits and unitary time-evolution
operators. The former is related to the study of Grassmann
manifolds.},
Doi = {10.1103/PhysRevLett.121.080406},
Key = {fds338335}
}
@article{fds340902,
Author = {Binder, M and Barthel, T},
Title = {Infinite boundary conditions for response functions and
limit cycles within the infinite-system density matrix
renormalization group approach demonstrated for
bilinear-biquadratic spin-1 chains},
Journal = {Physical Review B},
Volume = {98},
Number = {23},
Publisher = {American Physical Society (APS)},
Year = {2018},
Month = {December},
url = {http://dx.doi.org/10.1103/PhysRevB.98.235114},
Abstract = {Response functions (Âx(t)By(0)) for one-dimensional
strongly correlated quantum many-body systems can be
computed with matrix product state (MPS) techniques.
Especially, when one is interested in spectral functions or
dynamic structure factors of translation-invariant systems,
the response for some range |x-y|< is needed. We demonstrate
how the number of required time-evolution runs can be
reduced substantially: (a) If finite-system simulations are
employed, the number of time-evolution runs can be reduced
from to 2. (b) To go beyond, one can employ infinite MPS
(iMPS) such that two evolution runs suffice. To this
purpose, iMPS that are heterogeneous only around the causal
cone of the perturbation are evolved in time, i.e., the
simulation is done with infinite boundary conditions.
Computing overlaps of these states, spatially shifted
relative to each other, yields the response functions for
all distances |x-y|. As a specific application, we compute
the dynamic structure factor for ground states of
bilinear-biquadratic spin-1 chains with very high resolution
and explain the underlying low-energy physics. To determine
the initial uniform iMPS for such simulations,
infinite-system density matrix renormalization group (iDMRG)
can be employed. We discuss that, depending on the system
and chosen bond dimension, iDMRG with a cell size nc may
converge to a nontrivial limit cycle of length m. This then
corresponds to an iMPS with an enlarged unit cell of size
mnc.},
Doi = {10.1103/PhysRevB.98.235114},
Key = {fds340902}
}
@article{fds375959,
Author = {Miao, Q and Barthel, T},
Title = {Isometric tensor network optimization for extensive
Hamiltonians is free of barren plateaus},
Journal = {arXiv:2304.14320},
Year = {2023},
Month = {April},
url = {https://doi.org/10.48550/arXiv.2304.14320},
Abstract = {We explain why and numerically confirm that there are no
barren plateaus in the energy optimization of isometric
tensor network states (TNS) for extensive Hamiltonians with
finite-range interactions. Specifically, we consider matrix
product states, tree tensor network states, and the
multiscale entanglement renormalization ansatz. The variance
of the energy gradient, evaluated by taking the Haar average
over the TNS tensors, has a leading system-size independent
term and decreases according to a power law in the bond
dimension. For a hierarchical TNS with branching ratio b,
the variance of the gradient with respect to a tensor in
layer t scales as (br)^t, where r is the second largest
eigenvalue of the Haar-average doubled layer-transition
channel and decreases algebraically with increasing bond
dimension. The observed scaling properties of the gradient
variance bear implications for efficient initialization
procedures.},
Doi = {10.48550/arXiv.2304.14320},
Key = {fds375959}
}
@article{fds352587,
Author = {Binder, M and Barthel, T},
Title = {Low-energy physics of isotropic spin-1 chains in the
critical and Haldane phases},
Journal = {Physical Review B},
Volume = {102},
Number = {1},
Year = {2020},
Month = {July},
url = {http://dx.doi.org/10.1103/PhysRevB.102.014447},
Abstract = {Using a matrix product state algorithm with infinite
boundary conditions, we compute high-resolution dynamic spin
and quadrupolar structure factors in the thermodynamic limit
to explore the low-energy excitations of isotropic
bilinear-biquadratic spin-1 chains. Haldane mapped the
spin-1 Heisenberg antiferromagnet to a continuum field
theory, the nonlinear sigma model (NLσM). We find that the
NLσM fails to capture the influence of the biquadratic term
and provides only an unsatisfactory description of the
Haldane phase physics. But several features in the Haldane
phase can be explained by noninteracting multimagnon states.
The physics at the Uimin-Lai-Sutherland point is
characterized by multisoliton continua. Moving into the
extended critical phase, we find that these excitation
continua contract, which we explain using a field-theoretic
description. New excitations emerge at higher energies and,
in the vicinity of the purely biquadratic point, they show
simple cosine dispersions. Using block fidelities, we
identify them as elementary one-particle excitations and
relate them to the integrable Temperley-Lieb
chain.},
Doi = {10.1103/PhysRevB.102.014447},
Key = {fds352587}
}
@article{fds375958,
Author = {Chen, H and Barthel, T},
Title = {Machine learning with tree tensor networks, CP rank
constraints, and tensor dropout},
Journal = {arXiv:2305.19440},
Year = {2023},
Month = {May},
url = {https://doi.org/10.48550/arXiv.2305.19440},
Abstract = {Tensor networks approximate order-N tensors with a reduced
number of degrees of freedom that is only polynomial in N
and arranged as a network of partially contracted smaller
tensors. As suggested in [arXiv:2205.15296] in the context
of quantum many-body physics, computation costs can be
further substantially reduced by imposing constraints on the
canonical polyadic (CP) rank of the tensors in such
networks. Here we demonstrate how tree tensor networks (TTN)
with CP rank constraints and tensor dropout can be used in
machine learning. The approach is found to outperform other
tensor-network based methods in Fashion-MNIST image
classification. A low-rank TTN classifier with branching
ratio 4 reaches test set accuracy of 90.3 percent with low
computation costs. Consisting of mostly linear elements,
tensor network classifiers avoid the vanishing gradient
problem of deep neural networks. The CP rank constraints
have additional advantages: The number of parameters can be
decreased and tuned more freely to control overfitting,
improve generalization properties, and reduce computation
costs. They allow us to employ trees with large branching
ratios which substantially improves the representation
power.},
Doi = {10.48550/arXiv.2305.19440},
Key = {fds375958}
}
@article{fds302496,
Author = {Barthel, T and Kasztelan, C and McCulloch, IP and Schollwöck,
U},
Title = {Magnetism, coherent many-particle dynamics, and relaxation
with ultracold bosons in optical superlattices},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {79},
Number = {5},
Publisher = {American Physical Society (APS)},
Year = {2009},
Month = {May},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.79.053627},
Abstract = {We study how well magnetic models can be implemented with
ultracold bosonic atoms of two different hyperfine states in
an optical superlattice. The system is captured by a
two-species Bose-Hubbard model, but realizes in a certain
parameter regime actually the physics of a spin-1/2
Heisenberg magnet, describing the second-order hopping
processes. Tuning of the superlattice allows for controlling
the effect of fast first-order processes versus the slower
second-order ones. Using the density-matrix
renormalization-group method, we provide the evolution of
typical experimentally available observables. The validity
of the description via the Heisenberg model, depending on
the parameters of the Hubbard model, is studied numerically
and analytically. The analysis is also motivated by recent
experiments where coherent two-particle dynamics with
ultracold bosonic atoms in isolated double wells were
realized. We provide theoretical background for the next
step, the observation of coherent many-particle dynamics
after coupling the double wells. Contrary to the case of
isolated double wells, relaxation of local observables can
be observed. The tunability between the Bose-Hubbard model
and the Heisenberg model in this setup could be used to
study experimentally the differences in equilibration
processes for nonintegrable and Bethe ansatz integrable
models. We show that the relaxation in the Heisenberg model
is connected to a phase averaging effect, which is in
contrast to the typical scattering driven thermalization in
nonintegrable models. We discuss the preparation of magnetic
ground states by adiabatic tuning of the superlattice
parameters. © 2009 The American Physical
Society.},
Doi = {10.1103/PhysRevA.79.053627},
Key = {fds302496}
}
@article{fds332866,
Author = {Barthel, T and De Bacco and C and Franz, S},
Title = {Matrix product algorithm for stochastic dynamics on networks
applied to nonequilibrium Glauber dynamics},
Journal = {Physical Review E},
Volume = {97},
Number = {1},
Pages = {010104},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.97.010104},
Abstract = {We introduce and apply an efficient method for the precise
simulation of stochastic dynamical processes on locally
treelike graphs. Networks with cycles are treated in the
framework of the cavity method. Such models correspond, for
example, to spin-glass systems, Boolean networks, neural
networks, or other technological, biological, and social
networks. Building upon ideas from quantum many-body theory,
our approach is based on a matrix product approximation of
the so-called edge messages - conditional probabilities of
vertex variable trajectories. Computation costs and accuracy
can be tuned by controlling the matrix dimensions of the
matrix product edge messages (MPEM) in truncations. In
contrast to Monte Carlo simulations, the algorithm has a
better error scaling and works for both single instances as
well as the thermodynamic limit. We employ it to examine
prototypical nonequilibrium Glauber dynamics in the kinetic
Ising model. Because of the absence of cancellation effects,
observables with small expectation values can be evaluated
accurately, allowing for the study of decay processes and
temporal correlations.},
Doi = {10.1103/PhysRevE.97.010104},
Key = {fds332866}
}
@article{fds322472,
Author = {Barthel, T},
Title = {Matrix product purifications for canonical ensembles and
quantum number distributions},
Journal = {Physical Review B},
Volume = {94},
Number = {11},
Publisher = {American Physical Society (APS)},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.1103/PhysRevB.94.115157},
Abstract = {Matrix product purifications (MPPs) are a very efficient
tool for the simulation of strongly correlated quantum
many-body systems at finite temperatures. When a system
features symmetries, these can be used to reduce computation
costs substantially. It is straightforward to compute an MPP
of a grand-canonical ensemble, also when symmetries are
exploited. This paper provides and demonstrates methods for
the efficient computation of MPPs of canonical ensembles
under utilization of symmetries. Furthermore, we present a
scheme for the evaluation of global quantum number
distributions using matrix product density operators
(MPDOs). We provide exact matrix product representations for
canonical infinite-temperature states, and discuss how they
can be constructed alternatively by applying matrix product
operators to vacuum-type states or by using entangler
Hamiltonians. A demonstration of the techniques for
Heisenberg spin-1/2 chains explains why the difference in
the energy densities of canonical and grand-canonical
ensembles decays as 1/L.},
Doi = {10.1103/PhysRevB.94.115157},
Key = {fds322472}
}
@article{fds302490,
Author = {Binder, M and Barthel, T},
Title = {Minimally entangled typical thermal states versus matrix
product purifications for the simulation of equilibrium
states and time evolution},
Journal = {Physical Review B - Condensed Matter and Materials
Physics},
Volume = {92},
Number = {12},
Publisher = {American Physical Society (APS)},
Year = {2015},
Month = {September},
ISSN = {1098-0121},
url = {http://dx.doi.org/10.1103/PhysRevB.92.125119},
Abstract = {For the simulation of equilibrium states and
finite-temperature response functions of strongly correlated
quantum many-body systems, we compare the efficiencies of
two different approaches in the framework of the density
matrix renormalization group (DMRG). The first is based on
matrix product purifications. The second, more recent one,
is based on so-called minimally entangled typical thermal
states (METTS). For the latter, we highlight the interplay
of statistical and DMRG truncation errors, discuss the use
of self-averaging effects, and describe schemes for the
computation of response functions. For critical as well as
gapped phases of the spin-1/2 XXZ chain and the
one-dimensional Bose-Hubbard model, we assess the
computation costs and accuracies of the two methods at
different temperatures. For almost all considered cases, we
find that, for the same computation cost, purifications
yield more accurate results than METTS - often by orders of
magnitude. The METTS algorithm becomes more efficient only
for temperatures well below the system's energy gap. The
exponential growth of the computation cost in the evaluation
of response functions limits the attainable time scales in
both methods and we find that in this regard, METTS do not
outperform purifications.},
Doi = {10.1103/PhysRevB.92.125119},
Key = {fds302490}
}
@article{fds302497,
Author = {Lake, B and Tennant, DA and Caux, JS and Barthel, T and Schollwöck, U and Nagler, SE and Frost, CD},
Title = {Multispinon continua at zero and finite temperature in a
near-ideal heisenberg Chain},
Journal = {Physical Review Letters},
Volume = {111},
Number = {13},
Pages = {137205},
Year = {2013},
Month = {September},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.111.137205},
Abstract = {The space-and time-dependent response of many-body quantum
systems is the most informative aspect of their emergent
behavior. The dynamical structure factor, experimentally
measurable using neutron scattering, can map this response
in wave vector and energy with great detail, allowing
theories to be quantitatively tested to high accuracy. Here,
we present a comparison between neutron scattering
measurements on the one-dimensional spin-1/2 Heisenberg
antiferromagnet KCuF3, and recent state-of-the-art
theoretical methods based on integrability and density
matrix renormalization group simulations. The unprecedented
quantitative agreement shows that precise descriptions of
strongly correlated states at all distance, time, and
temperature scales are now possible, and highlights the need
to apply these novel techniques to other problems in
low-dimensional magnetism. © 2013 American Physical
Society.},
Doi = {10.1103/PhysRevLett.111.137205},
Key = {fds302497}
}
@article{fds368798,
Author = {Barthel, T and Lu, J and Friesecke, G},
Title = {On the closedness and geometry of tensor network state
sets},
Journal = {Letters in Mathematical Physics},
Volume = {112},
Number = {4},
Year = {2022},
Month = {August},
url = {http://dx.doi.org/10.1007/s11005-022-01552-z},
Abstract = {Tensor network states (TNS) are a powerful approach for the
study of strongly correlated quantum matter. The curse of
dimensionality is addressed by parametrizing the many-body
state in terms of a network of partially contracted tensors.
These tensors form a substantially reduced set of effective
degrees of freedom. In practical algorithms, functionals
like energy expectation values or overlaps are optimized
over certain sets of TNS. Concerning algorithmic stability,
it is important whether the considered sets are closed
because, otherwise, the algorithms may approach a boundary
point that is outside the TNS set and tensor elements
diverge. We discuss the closedness and geometries of TNS
sets, and we propose regularizations for optimization
problems on non-closed TNS sets. We show that sets of matrix
product states (MPS) with open boundary conditions, tree
tensor network states, and the multiscale entanglement
renormalization ansatz are always closed, whereas sets of
translation-invariant MPS with periodic boundary conditions
(PBC), heterogeneous MPS with PBC, and projected entangled
pair states are generally not closed. The latter is done
using explicit examples like the W state, states that we
call two-domain states, and fine-grained versions
thereof.},
Doi = {10.1007/s11005-022-01552-z},
Key = {fds368798}
}
@article{fds368750,
Author = {T. Barthel and J. Lu and G. Friesecke},
Title = {On the closedness and geometry of tensor network state
sets},
Journal = {Lett. Math. Phys.},
Volume = {72},
Pages = {112},
Year = {2022},
url = {http://dx.doi.org/10.1007/s11005-022-01552-z},
Abstract = {Tensor network states (TNS) are a powerful approach for the
study of strongly correlated quantum matter. The curse of
dimensionality is addressed by parametrizing the many-body
state in terms of a network of partially contracted tensors.
These tensors form a substantially reduced set of effective
degrees of freedom. In practical algorithms, functionals
like energy expectation values or overlaps are optimized
over certain sets of TNS. Concerning algorithmic stability,
it is important whether the considered sets are closed
because, otherwise, the algorithms may approach a boundary
point that is outside the TNS set and tensor elements
diverge. We discuss the closedness and geometries of TNS
sets, and we propose regularizations for optimization
problems on non-closed TNS sets. We show that sets of matrix
product states (MPS) with open boundary conditions, tree
tensor network states, and the multiscale entanglement
renormalization ansatz are always closed, whereas sets of
translation-invariant MPS with periodic boundary conditions
(PBC), heterogeneous MPS with PBC, and projected entangled
pair states are generally not closed. The latter is done
using explicit examples like the W state, states that we
call two-domain states, and fine-grained versions
thereof.},
Doi = {10.1007/s11005-022-01552-z},
Key = {fds368750}
}
@article{fds361138,
Author = {Barthel, T},
Title = {One-dimensional quantum systems at finite temperatures can
be simulated efficiently on classical computers},
Journal = {arXiv:1708.09349},
Year = {2017},
Month = {August},
Abstract = {It is by now well-known that ground states of gapped
one-dimensional (1d) quantum-many body systems with
short-range interactions can be studied efficiently using
classical computers and matrix product state techniques. A
corresponding result for finite temperatures was missing.
Using the replica trick in 1+1d quantum field theory, it is
shown here that the cost for the classical simulation of 1d
systems at finite temperatures grows in fact only
polynomially with the inverse temperature and is system-size
independent -- even for gapless systems. In particular, we
show that the thermofield double state (TDS), a purification
of the equilibrium density operator, can be obtained
efficiently in matrix-product form. The argument is based on
the scaling behavior of Rényi entanglement entropies in the
TDS. At finite temperatures, they obey the area law. For
gapless systems with central charge $c$, the entanglement is
found to grow only logarithmically with inverse temperature,
$S_\alpha\sim \frac{c}{6}(1+1/\alpha)\log \beta$. The
field-theoretical results are tested and confirmed by
quasi-exact numerical computations for integrable and
non-integrable spin systems, and interacting
bosons.},
Key = {fds361138}
}
@article{fds347981,
Author = {Barthel, T and Zhang, Y},
Title = {Optimized Lie–Trotter–Suzuki decompositions for two and
three non-commuting terms},
Journal = {Annals of Physics},
Volume = {418},
Pages = {168165-168165},
Publisher = {Elsevier Masson},
Year = {2020},
Month = {July},
url = {http://arxiv.org/abs/1901.04974},
Abstract = {Lie–Trotter–Suzuki decompositions are an efficient way
to approximate operator exponentials exp(tH) when H is a sum
of n (non-commuting) terms which, individually, can be
exponentiated easily. They are employed in time-evolution
algorithms for tensor network states, digital quantum
simulation protocols, path integral methods like quantum
Monte Carlo, and splitting methods for symplectic
integrators in classical Hamiltonian systems. We provide
optimized decompositions up to order t6. The leading error
term is expanded in nested commutators (Hall bases) and we
minimize the 1-norm of the coefficients. For n=2 terms,
several of the optima we find are close to those in
McLachlan (1995). Generally, our results substantially
improve over unoptimized decompositions by Forest, Ruth,
Yoshida, and Suzuki. We explain why these decompositions are
sufficient to efficiently simulate any one- or
two-dimensional lattice model with finite-range
interactions. This follows by solving a partitioning problem
for the interaction graph.},
Doi = {10.1016/j.aop.2020.168165},
Key = {fds347981}
}
@article{fds318403,
Author = {Schlittler, T and Barthel, T and Misguich, G and Vidal, J and Mosseri,
R},
Title = {Phase diagram of an extended quantum dimer model on the
hexagonal lattice},
Journal = {Physical Review Letters},
Volume = {115},
Number = {21},
Pages = {217202},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.1103/PhysRevLett.115.217202},
Abstract = {We introduce a quantum dimer model on the hexagonal lattice
that, in addition to the standard three-dimer kinetic and
potential terms, includes a competing potential part
counting dimer-free hexagons. The zero-temperature phase
diagram is studied by means of quantum Monte Carlo
simulations, supplemented by variational arguments. It
reveals some new crystalline phases and a cascade of
transitions with rapidly changing flux (tilt in the height
language). We analyze perturbatively the vicinity of the
Rokhsar-Kivelson point, showing that this model has the
microscopic ingredients needed for the "devil's staircase"
scenario [Eduardo Fradkin et al. Phys. Rev. B 69, 224415
(2004)], and is therefore expected to produce fractal
variations of the ground-state flux.},
Doi = {10.1103/PhysRevLett.115.217202},
Key = {fds318403}
}
@article{fds329759,
Author = {Schlittler, TM and Mosseri, R and Barthel, T},
Title = {Phase diagram of the hexagonal lattice quantum dimer model:
Order parameters, ground-state energy, and
gaps},
Journal = {Physical Review B},
Volume = {96},
Number = {19},
Pages = {195142-195142},
Publisher = {American Physical Society (APS)},
Year = {2017},
Month = {November},
url = {http://dx.doi.org/10.1103/PhysRevB.96.195142},
Abstract = {The phase diagram of the quantum dimer model on the
hexagonal (honeycomb) lattice is computed numerically,
extending on earlier work by Moessner, Sondhi, and Chandra.
The different ground state phases are studied in detail
using several local and global observables. In addition, we
analyze imaginary-time correlation functions to determine
ground state energies as well as gaps to the first excited
states. This leads in particular to a confirmation that the
intermediary so-called plaquette phase is gapped. On the
technical side, we describe an efficient world-line quantum
Monte Carlo algorithm with improved cluster updates that
increase acceptance probabilities by taking account of
potential terms of the Hamiltonian during the cluster
construction. The Monte Carlo simulations are supplemented
with variational computations.},
Doi = {10.1103/PhysRevB.96.195142},
Key = {fds329759}
}
@article{fds302500,
Author = {Barthel, T},
Title = {Precise evaluation of thermal response functions by
optimized density matrix renormalization group
schemes},
Journal = {New Journal of Physics},
Volume = {15},
Number = {7},
Pages = {073010-073010},
Publisher = {IOP Publishing},
Year = {2013},
Month = {July},
url = {http://dx.doi.org/10.1088/1367-2630/15/7/073010},
Abstract = {This paper provides a study and discussion of earlier as
well as novel more efficient schemes for the precise
evaluation of finite-temperature response functions of
strongly correlated quantum systems in the framework of the
time-dependent density matrix renormalization group (tDMRG).
The computational costs and bond dimensions as functions of
time and temperature are examined for the example of the
spin-1/2 XXZ Heisenberg chain in the critical XY phase and
the gapped Néel phase. The matrix product state
purifications occurring in the algorithms are in a
one-to-one relation with the corresponding matrix product
operators. This notational simplification elucidates
implications of quasi-locality on the computational costs.
Based on the observation that there is considerable freedom
in designing efficient tDMRG schemes for the calculation of
dynamical correlators at finite temperatures, a new class of
optimizable schemes, as recently suggested in Barthel,
Schollwöck and Sachdev (2012 arXiv:1212.3570), is explained
and analyzed numerically. A specific novel near-optimal
scheme that requires no additional optimization reaches
maximum times that are typically increased by a factor of 2,
when compared against earlier approaches. These increased
reachable times make many more physical applications
accessible. For each of the described tDMRG schemes, one can
devise a corresponding transfer matrix renormalization group
variant. © IOP Publishing and Deutsche Physikalische
Gesellschaft.},
Doi = {10.1088/1367-2630/15/7/073010},
Key = {fds302500}
}
@article{fds361136,
Author = {Miao, Q and Barthel, T},
Title = {Quantum-classical eigensolver using multiscale entanglement
renormalization},
Journal = {Physical Review Research},
Volume = {5},
Number = {3},
Year = {2023},
Month = {July},
url = {http://arxiv.org/abs/2108.13401},
Abstract = {We propose a variational quantum eigensolver (VQE) for the
simulation of strongly correlated quantum matter based on a
multiscale entanglement renormalization ansatz (MERA) and
gradient-based optimization. This MERA quantum eigensolver
can have substantially lower computation costs than
corresponding classical algorithms. Due to its narrow causal
cone, the algorithm can be implemented on noisy
intermediate-scale quantum (NISQ) devices and still describe
large systems. It is particularly attractive for ion-trap
devices with ion-shuttling capabilities. The number of
required qubits is system-size independent and increases
only to a logarithmic scaling when using quantum amplitude
estimation to speed up gradient evaluations. Translation
invariance can be used to make computation costs
square-logarithmic in the system size and describe the
thermodynamic limit. We demonstrate the approach numerically
for a MERA with Trotterized disentanglers and isometries.
With a few Trotter steps, one recovers the accuracy of the
full MERA.},
Doi = {10.1103/PhysRevResearch.5.033141},
Key = {fds361136}
}
@article{fds302495,
Author = {Barthel, T and Kliesch, M},
Title = {Quasilocality and efficient simulation of Markovian quantum
dynamics},
Journal = {Physical Review Letters},
Volume = {108},
Number = {23},
Pages = {230504},
Year = {2012},
Month = {June},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.108.230504},
Abstract = {We consider open many-body systems governed by a
time-dependent quantum master equation with short-range
interactions. With a generalized Lieb-Robinson bound, we
show that the evolution in this very generic framework is
quasilocal; i.e., the evolution of observables can be
approximated by implementing the dynamics only in a vicinity
of the observables' support. The precision increases
exponentially with the diameter of the considered subsystem.
Hence, time evolution can be simulated on classical
computers with a cost that is independent of the system
size. Providing error bounds for Trotter decompositions, we
conclude that the simulation on a quantum computer is
additionally efficient in time. For experiments and
simulations in the Schrödinger picture, our result can be
used to rigorously bound finite-size effects. © 2012
American Physical Society.},
Doi = {10.1103/PhysRevLett.108.230504},
Key = {fds302495}
}
@article{fds302489,
Author = {Roux, G and Barthel, T and McCulloch, IP and Kollath, C and Schollwöck,
U and Giamarchi, T},
Title = {Quasiperiodic Bose-Hubbard model and localization in
one-dimensional cold atomic gases},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {78},
Number = {2},
Publisher = {American Physical Society (APS)},
Year = {2008},
Month = {August},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.78.023628},
Abstract = {We compute the phase diagram of the one-dimensional
Bose-Hubbard model with a quasiperiodic potential by means
of the density-matrix renormalization group technique. This
model describes the physics of cold atoms loaded in an
optical lattice in the presence of a superlattice potential
whose wavelength is incommensurate with the main lattice
wavelength. After discussing the conditions under which the
model can be realized experimentally, the study of the
density vs the chemical potential curves for a nontrapped
system unveils the existence of gapped phases at
incommensurate densities interpreted as incommensurate
charge-density-wave phases. Furthermore, a localization
transition is known to occur above a critical value of the
potential depth V2 in the case of free and hard-core bosons.
We extend these results to soft-core bosons for which the
phase diagrams at fixed densities display new features
compared with the phase diagrams known for random box
distribution disorder. In particular, a direct transition
from the superfluid phase to the Mott-insulating phase is
found at finite V2. Evidence for reentrances of the
superfluid phase upon increasing interactions is presented.
We finally comment on different ways to probe the emergent
quantum phases and most importantly, the existence of a
critical value for the localization transition. The latter
feature can be investigated by looking at the expansion of
the cloud after releasing the trap. © 2008 The American
Physical Society.},
Doi = {10.1103/PhysRevA.78.023628},
Key = {fds302489}
}
@article{fds302488,
Author = {Barthel, T and Kliesch, M and Eisert, J},
Title = {Real-space renormalization yields finite
correlations.},
Journal = {Physical review letters},
Volume = {105},
Number = {1},
Pages = {010502},
Publisher = {American Physical Society (APS)},
Year = {2010},
Month = {July},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/physrevlett.105.010502},
Abstract = {Real-space renormalization approaches for quantum lattice
systems generate certain hierarchical classes of states that
are subsumed by the multiscale entanglement renormalization
Ansatz (MERA). It is shown that, with the exception of one
spatial dimension, MERA states are actually states with
finite correlations, i.e., projected entangled pair states
(PEPS) with a bond dimension independent of the system size.
Hence, real-space renormalization generates states which can
be encoded with local effective degrees of freedom, and MERA
states form an efficiently contractible class of PEPS that
obey the area law for the entanglement entropy. It is
further pointed out that there exist other efficiently
contractible schemes violating the area law.},
Doi = {10.1103/physrevlett.105.010502},
Key = {fds302488}
}
@article{fds360765,
Author = {T. Barthel and Q. Miao},
Title = {Scaling functions for eigenstate entanglement crossovers in
harmonic lattices},
Journal = {Phys. Rev. A 104},
Volume = {104},
Pages = {022414},
Year = {2021},
Month = {September},
url = {http://dx.doi.org/10.1103/PhysRevA.104.022414},
Doi = {10.1103/PhysRevA.104.022414},
Key = {fds360765}
}
@article{fds347979,
Author = {Barthel, T and Miao, Q},
Title = {Scaling functions for eigenstate entanglement crossovers in
harmonic lattices},
Journal = {Physical Review A},
Volume = {104},
Number = {2},
Year = {2021},
Month = {August},
url = {http://arxiv.org/abs/1912.10045},
Abstract = {For quantum matter, eigenstate entanglement entropies obey
an area law or log-area law at low energies and small
subsystem sizes and cross over to volume laws for high
energies and large subsystems. This transition is captured
by crossover functions, which assume a universal scaling
form in quantum critical regimes. We demonstrate this for
the harmonic lattice model, which describes quantized
lattice vibrations and is a regularization for free scalar
field theories, modeling, e.g., spin-0 bosonic particles. In
one dimension, the ground-state entanglement obeys a
log-area law. For dimensions d≥2, it displays area laws,
even at criticality. The distribution of excited-state
entanglement entropies is found to be sharply peaked around
subsystem entropies of corresponding thermodynamic ensembles
in accordance with the eigenstate thermalization hypothesis.
Numerically, we determine crossover scaling functions for
the quantum critical regime of the model and do a
large-deviation analysis. We show how infrared singularities
of the system can be handled and how to access the
thermodynamic limit using a perturbative trick for the
covariance matrix. Eigenstates for quasi-free bosonic
systems are not Gaussian. We resolve this problem by
considering appropriate squeezed states instead. For these,
entanglement entropies can be evaluated efficiently.},
Doi = {10.1103/PhysRevA.104.022414},
Key = {fds347979}
}
@article{fds302494,
Author = {Barthel, T and Hübener, R},
Title = {Solving condensed-matter ground-state problems by
semidefinite relaxations},
Journal = {Physical Review Letters},
Volume = {108},
Number = {20},
Pages = {200404},
Year = {2012},
Month = {May},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.108.200404},
Abstract = {We present a generic approach to the condensed-matter
ground-state problem which is complementary to variational
techniques and works directly in the thermodynamic limit.
Relaxing the ground-state problem, we obtain semidefinite
programs (SDP). These can be solved efficiently, yielding
strict lower bounds to the ground-state energy and
approximations to the few-particle Green's functions. As the
method is applicable for all particle statistics, it
represents, in particular, a novel route for the study of
strongly correlated fermionic and frustrated spin systems in
D>1 spatial dimensions. It is demonstrated for the XXZ model
and the Hubbard model of spinless fermions. The results are
compared against exact solutions, quantum MonteCarlo
calculations, and Anderson bounds, showing the
competitiveness of the SDP method. © 2012 American Physical
Society.},
Doi = {10.1103/PhysRevLett.108.200404},
Key = {fds302494}
}
@article{fds368797,
Author = {Barthel, T and Zhang, Y},
Title = {Solving quasi-free and quadratic Lindblad master equations
for open fermionic and bosonic systems},
Journal = {Journal of Statistical Mechanics: Theory and
Experiment},
Volume = {2022},
Number = {11},
Pages = {113101},
Year = {2022},
Month = {November},
url = {http://dx.doi.org/10.1088/1742-5468/ac8e5c},
Abstract = {The dynamics of Markovian open quantum systems are described
by Lindblad master equations. For fermionic and bosonic
systems that are quasi-free, i.e. with Hamiltonians that are
quadratic in the ladder operators and Lindblad operators
that are linear in the ladder operators, we derive the
equation of motion for the covariance matrix. This
determines the evolution of Gaussian initial states and the
steady states, which are also Gaussian. Using ladder
super-operators (a.k.a. third quantization), we show how the
Liouvillian can be transformed to a many-body Jordan normal
form which also reveals the full many-body spectrum.
Extending previous work by Prosen and Seligman, we treat
fermionic and bosonic systems on equal footing with Majorana
operators, shorten and complete some derivations, also
address the odd-parity sector for fermions, give a criterion
for the existence of bosonic steady states, cover
non-diagonalizable Liouvillians also for bosons, and include
quadratic systems. In extension of the quasi-free open
systems, quadratic open systems comprise additional
Hermitian Lindblad operators that are quadratic in the
ladder operators. While Gaussian states may then evolve into
non-Gaussian states, the Liouvillian can still be
transformed to a useful block-triangular form, and the
equations of motion for k-point Green’s functions form a
closed hierarchy. Based on this formalism, results on
criticality and dissipative phase transitions in such models
are discussed in a companion paper.},
Doi = {10.1088/1742-5468/ac8e5c},
Key = {fds368797}
}
@article{fds302501,
Author = {Barthel, T and Schollwöck, U and White, SR},
Title = {Spectral functions in one-dimensional quantum systems at
finite temperature using the density matrix renormalization
group},
Journal = {Physical Review B - Condensed Matter and Materials
Physics},
Volume = {79},
Number = {24},
Publisher = {American Physical Society (APS)},
Year = {2009},
Month = {June},
ISSN = {1098-0121},
url = {http://dx.doi.org/10.1103/PhysRevB.79.245101},
Abstract = {We present time-dependent density matrix renormalization
group simulations (t-DMRG) at finite temperatures. It is
demonstrated how a combination of finite-temperature t-DMRG
and time-series prediction allows for an easy and very
accurate calculation of spectral functions in
one-dimensional quantum systems, irrespective of their
statistics for arbitrary temperatures. This is illustrated
with spin structure factors of XX and XXX spin- 1 2 chains.
For the XX model we can compare against an exact solution,
and for the XXX model (Heisenberg antiferromagnet) against a
Bethe ansatz solution and quantum Monte Carlo data. © 2009
The American Physical Society.},
Doi = {10.1103/PhysRevB.79.245101},
Key = {fds302501}
}
@article{fds368799,
Author = {Barthel, T and Zhang, Y},
Title = {Superoperator structures and no-go theorems for dissipative
quantum phase transitions},
Journal = {Physical Review A},
Volume = {105},
Number = {5},
Pages = {052224},
Year = {2022},
Month = {May},
url = {http://dx.doi.org/10.1103/PhysRevA.105.052224},
Abstract = {In the thermodynamic limit, the steady states of open
quantum many-body systems can undergo nonequilibrium phase
transitions due to a competition between coherent and
driven-dissipative dynamics. Here, we consider Markovian
systems and elucidate structures of the Liouville
superoperator that generates the time evolution. In many
cases of interest, an operator-basis transformation can
bring the Liouvillian into a block-triangular form, making
it possible to assess its spectrum. The spectral gap sets
the asymptotic decay rate. The superoperator structure can
be used to bound gaps from below, showing that, in a large
class of systems, dissipative phase transitions are actually
impossible and that the convergence to steady states follows
an exponential temporal decay. Furthermore, when the blocks
on the diagonal are Hermitian, the Liouvillian spectra obey
Weyl ordering relations. The results apply, for example, to
Davies generators and quadratic systems and are also
demonstrated for various spin models.},
Doi = {10.1103/PhysRevA.105.052224},
Key = {fds368799}
}
@article{fds326914,
Author = {Binder, M and Barthel, T},
Title = {Symmetric minimally entangled typical thermal states for
canonical and grand-canonical ensembles},
Journal = {Physical Review B},
Volume = {95},
Number = {19},
Publisher = {American Physical Society (APS)},
Year = {2017},
Month = {May},
url = {http://dx.doi.org/10.1103/PhysRevB.95.195148},
Abstract = {Based on the density matrix renormalization group (DMRG),
strongly correlated quantum many-body systems at finite
temperatures can be simulated by sampling over a certain
class of pure matrix product states (MPS) called minimally
entangled typical thermal states (METTS). When a system
features symmetries, these can be utilized to substantially
reduce MPS computation costs. It is conceptually
straightforward to simulate canonical ensembles using
symmetric METTS. In practice, it is important to alternate
between different symmetric collapse bases to decrease
autocorrelations in the Markov chain of METTS. To this
purpose, we introduce symmetric Fourier and Haar-random
block bases that are efficiently mixing. We also show how
grand-canonical ensembles can be simulated efficiently with
symmetric METTS. We demonstrate these approaches for
spin-1/2 XXZ chains and discuss how the choice of the
collapse bases influences autocorrelations as well as the
distribution of measurement values and, hence, convergence
speeds.},
Doi = {10.1103/PhysRevB.95.195148},
Key = {fds326914}
}
@article{fds368761,
Author = {Chen, H and Barthel, T},
Title = {Tensor Network States with Low-Rank Tensors},
Journal = {arXiv:2205.15296},
Year = {2022},
Month = {May},
url = {http://arxiv.org/abs/2205.15296},
Abstract = {Tensor networks are used to efficiently approximate states
of strongly-correlated quantum many-body systems. More
generally, tensor network approximations may allow to reduce
the costs for operating on an order-N tensor from
exponential to polynomial in N, and this has become a
popular approach for machine learning. We introduce the idea
of imposing low-rank constraints on the tensors that compose
the tensor network. With this modification, the time and
space complexities for the network optimization can be
substantially reduced while maintaining high accuracy. We
detail this idea for tree tensor network states (TTNS) and
projected entangled-pair states. Simulations of spin models
on Cayley trees with low-rank TTNS exemplify the effect of
rank constraints on the expressive power. We find that
choosing the tensor rank r to be on the order of the bond
dimension m, is sufficient to obtain high-accuracy
groundstate approximations and to substantially outperform
standard TTNS computations. Thus low-rank tensor networks
are a promising route for the simulation of quantum matter
and machine learning on large data sets.},
Doi = {10.48550/arXiv.2205.15296},
Key = {fds368761}
}
@article{fds347980,
Author = {Barthel, T},
Title = {The matrix product approximation for the dynamic cavity
method},
Journal = {Journal of Statistical Mechanics: Theory and
Experiment},
Volume = {2020},
Number = {1},
Pages = {013217-013217},
Publisher = {IOP Publishing},
Year = {2020},
Month = {January},
url = {http://arxiv.org/abs/1904.03312},
Abstract = {Stochastic dynamics of classical degrees of freedom, defined
on vertices of locally tree-like graphs, can be studied in
the framework of the dynamic cavity method which is exact
for tree graphs. Such models correspond for example to
spin-glass systems, Boolean networks, neural networks, and
other technical, biological, and social networks. The
central objects in the cavity method are edge messages -
conditional probabilities of two vertex variable
trajectories. In this paper, we discuss a rather pedagogical
derivation for the dynamic cavity method, give a detailed
account of the novel matrix product edge message (MPEM)
algorithm for the solution of the dynamic cavity equation as
introduced in Barthel et al (2018 Phys. Rev. E 97 010104
(R)), and present optimizations and extensions. Matrix
product approximations of the edge messages are constructed
recursively in an iteration over time. Computation costs and
precision can be tuned by controlling the matrix dimensions
of the MPEM in truncations. Without truncations, the
dynamics is exact. Data for Glauber-Ising dynamics shows a
linear growth of computation costs in time. In contrast to
Monte Carlo simulations, the approach has a much better
error scaling. Hence, it gives for example access to low
probability events and decaying observables like temporal
correlations. We discuss optimized truncation schemes and an
extension that allows to capture models which have a
continuum time limit.},
Doi = {10.1088/1742-5468/ab5701},
Key = {fds347980}
}
@article{fds302482,
Author = {Pineda, C and Barthel, T and Eisert, J},
Title = {Unitary circuits for strongly correlated
fermions},
Journal = {Physical Review A - Atomic, Molecular, and Optical
Physics},
Volume = {81},
Number = {5},
Publisher = {American Physical Society (APS)},
Year = {2010},
Month = {May},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.81.050303},
Abstract = {We introduce a scheme for efficiently describing pure states
of strongly correlated fermions in higher dimensions using
unitary circuits featuring a causal cone. A local way of
computing local expectation values is presented. We
formulate a dynamical reordering scheme, corresponding to
time-adaptive Jordan-Wigner transformation, that avoids
nonlocal string operators. Primitives of such a reordering
scheme are highlighted. Fermionic unitary circuits can be
contracted with the same complexity as in the spin case. The
scheme gives rise to a variational description of fermionic
models not suffering from a sign problem. We present
numerical examples in a 9×9 and 6×6 fermionic lattice
model to show the functioning of the approach. © 2010 The
American Physical Society.},
Doi = {10.1103/PhysRevA.81.050303},
Key = {fds302482}
}
%% Papers Accepted
@article{fds375148,
Author = {Q. Miao and T. Barthel},
Title = {Quantum-classical eigensolver using multiscale entanglement
renormalization},
Journal = {Phys. Rev. Res.},
Volume = {5},
Pages = {033141},
Year = {2023},
url = {http://dx.doi.org/10.1103/PhysRevResearch.5.033141},
Abstract = {We propose a variational quantum eigensolver (VQE) for the
simulation of strongly correlated quantum matter based on a
multiscale entanglement renormalization ansatz (MERA) and
gradient-based optimization. This MERA quantum eigensolver
can have substantially lower computation costs than
corresponding classical algorithms. Due to its narrow causal
cone, the algorithm can be implemented on noisy
intermediate-scale quantum (NISQ) devices and still describe
large systems. It is particularly attractive for ion-trap
devices with ion-shuttling capabilities. The number of
required qubits is system-size independent and increases
only to a logarithmic scaling when using quantum amplitude
estimation to speed up gradient evaluations. Translation
invariance can be used to make computation costs
square-logarithmic in the system size and describe the
thermodynamic limit. We demonstrate the approach numerically
for a MERA with Trotterized disentanglers and isometries.
With a few Trotter steps, one recovers the accuracy of the
full MERA.},
Doi = {10.1103/PhysRevResearch.5.033141},
Key = {fds375148}
}
%% Papers Submitted
@article{fds360766,
Author = {T. Barthel and J. Lu and G. Friesecke},
Title = {On the closedness and geometry of tensor network state
sets},
Journal = {arXiv:2108.00031},
Year = {2021},
Month = {August},
url = {http://arxiv.org/abs/2108.00031},
Key = {fds360766}
}
@article{fds360768,
Author = {T. Barthel and Y. Zhang},
Title = {Solving quasi-free and quadratic Lindblad master equations
for open fermionic and bosonic systems},
Journal = {arXiv:2112.08344},
Year = {2021},
Month = {December},
url = {http://arxiv.org/abs/2112.08344},
Key = {fds360768}
}