%% @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 = {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 = {© 2014 IOP Publishing Ltd and SISSA Medialab srl. 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 SMAXbecomes inaccurate. For highly-entangled states SA∝ Lc, with Lcthe 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}, 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{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}, 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{fds302485, Author = {Zhou, HQ and Barthel, T and Fjærestad, JO and Schollwöck, U}, Title = {Entanglement and boundary critical phenomena}, Journal = {Physical Review A}, 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}, 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 = {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 = {© 2016 American Physical Society. 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 = {© 2018 American Physical Society. 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}, Doi = {10.1103/physrevb.98.235114}, Key = {fds340902} } @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}, 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 = {1-1}, 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 = {© 2016 American Physical Society. 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}, 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 = {© 2015 American Physical Society. 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{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 = {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. For 1d systems that can be described by a local 1+1d field theory, it is shown here that the cost for the classical simulation at finite temperatures grows in fact only polynomially with the inverse temperature and is system-size independent -- even for quantum critical 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 R\'{e}nyi entanglement entropies in the TDS. At finite temperatures, they obey the area law. For quantum critical systems, the entanglement is found to grow only logarithmically with inverse temperature, S~log(beta). The field-theoretical results are confirmed by quasi-exact numerical simulations of quantum magnets and interacting bosons.}, 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{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}, 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}, 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. © 2010 The American Physical Society.}, Doi = {10.1103/PhysRevLett.105.010502}, Key = {fds302488} } @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{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}, 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{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 = {© 2017 American Physical Society. 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{fds302482, Author = {Pineda, C and Barthel, T and Eisert, J}, Title = {Unitary circuits for strongly correlated fermions}, Journal = {Physical Review A}, 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} }