%% @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{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}, 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{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}, Year = {2017}, Month = {May}, url = {http://dx.doi.org/10.1103/PhysRevB.95.195148}, Doi = {10.1103/PhysRevB.95.195148}, Key = {fds326914} } @article{fds322472, Author = {Barthel, T}, Title = {Matrix product purifications for canonical ensembles and quantum number distributions}, Journal = {Physical Review B}, Volume = {94}, Number = {11}, Year = {2016}, Month = {September}, url = {http://dx.doi.org/10.1103/PhysRevB.94.115157}, Doi = {10.1103/PhysRevB.94.115157}, Key = {fds322472} } @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}, Year = {2016}, Month = {March}, url = {http://dx.doi.org/10.1103/PhysRevA.93.033650}, Doi = {10.1103/PhysRevA.93.033650}, Key = {fds318402} } @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{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}, Year = {2015}, Month = {September}, ISSN = {1098-0121}, url = {http://dx.doi.org/10.1103/PhysRevB.92.125119}, Doi = {10.1103/PhysRevB.92.125119}, Key = {fds302490} } @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 (Online)}, Volume = {2014}, Number = {10}, Pages = {P10029-P10029}, Year = {2014}, Month = {October}, url = {http://dx.doi.org/10.1088/1742-5468/2014/10/P10029}, Doi = {10.1088/1742-5468/2014/10/P10029}, Key = {fds318404} } @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}, Year = {2014}, Month = {June}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.89.063603}, Doi = {10.1103/PhysRevA.89.063603}, Key = {fds302499} } @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.}, Doi = {10.1103/physrevlett.111.150403}, Key = {fds302498} } @article{fds302497, Author = {Lake, B and Tennant, DA and Caux, J-S 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.}, Doi = {10.1103/physrevlett.111.137205}, Key = {fds302497} } @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}, Year = {2013}, Month = {July}, url = {http://dx.doi.org/10.1088/1367-2630/15/7/073010}, Doi = {10.1088/1367-2630/15/7/073010}, Key = {fds302500} } @article{fds302483, Author = {Kliesch, M and Barthel, T and Gogolin, C and Kastoryano, M and Eisert, J}, Title = {Erratum: Dissipative Quantum Church-Turing Theorem [Phys. Rev. Lett. 107 , 120501 (2011)]}, Journal = {Physical Review Letters}, Volume = {109}, Number = {11}, 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{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.}, Doi = {10.1103/physrevlett.108.230504}, Key = {fds302495} } @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 Monte Carlo calculations, and Anderson bounds, showing the competitiveness of the SDP method.}, Doi = {10.1103/physrevlett.108.200404}, Key = {fds302494} } @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.}, Doi = {10.1103/physrevlett.107.120501}, Key = {fds302493} } @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}, Year = {2010}, Month = {July}, ISSN = {0031-9007}, url = {http://dx.doi.org/10.1103/PhysRevLett.105.010502}, Doi = {10.1103/PhysRevLett.105.010502}, Key = {fds302488} } @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}, Year = {2010}, Month = {May}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.81.050303}, Doi = {10.1103/PhysRevA.81.050303}, Key = {fds302482} } @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}, Year = {2009}, Month = {October}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.80.042333}, Doi = {10.1103/PhysRevA.80.042333}, Key = {fds302487} } @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}, Year = {2009}, Month = {June}, ISSN = {1098-0121}, url = {http://dx.doi.org/10.1103/PhysRevB.79.245101}, Doi = {10.1103/PhysRevB.79.245101}, Key = {fds302501} } @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}, Year = {2009}, Month = {May}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.79.053627}, Doi = {10.1103/PhysRevA.79.053627}, Key = {fds302496} } @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}, Year = {2008}, Month = {August}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.78.023628}, Doi = {10.1103/PhysRevA.78.023628}, Key = {fds302489} } @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.}, Doi = {10.1103/physrevlett.100.100601}, Key = {fds302492} } @article{fds302484, Author = {Vidal, J and Dusuel, S and Barthel, T}, Title = {Entanglement entropy in collective models}, Journal = {Journal of statistical mechanics (Online)}, Volume = {2007}, Number = {01}, Pages = {P01015-P01015}, Year = {2007}, Month = {January}, url = {http://dx.doi.org/10.1088/1742-5468/2007/01/P01015}, Doi = {10.1088/1742-5468/2007/01/P01015}, Key = {fds302484} } @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 = {December}, 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.}, Doi = {10.1103/physrevlett.97.220402}, Key = {fds302491} } @article{fds302485, Author = {Zhou, H-Q 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}, Year = {2006}, Month = {November}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.74.050305}, Doi = {10.1103/PhysRevA.74.050305}, Key = {fds302485} } @article{fds302486, Author = {Barthel, T and Chung, M-C 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}, Year = {2006}, Month = {August}, ISSN = {1050-2947}, url = {http://dx.doi.org/10.1103/PhysRevA.74.022329}, Doi = {10.1103/PhysRevA.74.022329}, Key = {fds302486} }