Thomas Barthel

Journal Article Physical Review A · May 1, 2024 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, which are, for example, typical in condensed matter phys ... Full text Cite

Criteria for Davies irreducibility of Markovian quantum dynamics

Journal Article Journal of Physics A: Mathematical and Theoretical · March 15, 2024 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 invaria ... Full text Cite

Driven-dissipative Bose-Einstein condensation and the upper critical dimension

Journal Article Physical Review A · February 1, 2024 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-cor ... Full text Cite

Machine learning with tree tensor networks, CP rank constraints, and tensor dropout

Journal Article IEEE Transactions on Pattern Analysis and Machine Intelligence · January 1, 2024 Tensor networks developed in the context of condensed matter physics try to 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 we have r ... Full text Cite

Driven-dissipative Bose-Einstein condensation and the upper critical dimension

Journal Article arXiv:2311.13561 · November 22, 2023 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-cor ... Full text Link to item Cite

Criteria for Davies irreducibility of Markovian quantum dynamics

Journal Article arXiv:2310.17641 · October 26, 2023 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 invari ... Full text Cite

Quantum-classical eigensolver using multiscale entanglement renormalization

Journal Article Physical Review Research · July 1, 2023 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 substantial ... Full text Cite

Machine learning with tree tensor networks, CP rank constraints, and tensor dropout

Journal Article arXiv:2305.19440 · May 30, 2023 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 p ... Full text Cite

Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Journal Article arXiv:2304.14320 · April 27, 2023 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 te ... Full text Link to item Cite

Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states

Journal Article arXiv:2304.00161 · March 31, 2023 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 fo ... Full text Link to item Cite

Convergence and quantum advantage of Trotterized MERA for strongly-correlated systems

Journal Article arXiv:2303.08910 · March 15, 2023 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 certa ... Full text Link to item Cite

Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems

Journal Article Journal of Statistical Mechanics: Theory and Experiment · November 1, 2022 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 th ... Full text Cite

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

Journal Article Physical Review Letters · September 16, 2022 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. T ... Full text Cite

On the closedness and geometry of tensor network state sets

Journal Article Letters in Mathematical Physics · August 1, 2022 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 ... Full text Cite

Tensor Network States with Low-Rank Tensors

Journal Article arXiv:2205.15296 · May 30, 2022 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, ... Full text Link to item Cite

Superoperator structures and no-go theorems for dissipative quantum phase transitions

Journal Article Physical Review A · May 1, 2022 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 ... Full text Cite

Eigenstate entanglement scaling for critical interacting spin chains

Journal Article Quantum · January 1, 2022 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, t ... Full text Cite

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

Journal Article Physical Review A · August 1, 2021 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 ... Full text Cite

Eigenstate Entanglement: Crossover from the Ground State to Volume Laws

Journal Article Physical Review Letters · July 23, 2021 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 fu ... Full text Cite

Eigenstate entanglement scaling for critical interacting spin chains

Journal Article arXiv:2010.07265 · October 14, 2020 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, t ... Link to item Cite

Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Criteria for Davies irreducibility of Markovian quantum dynamics

Driven-dissipative Bose-Einstein condensation and the upper critical dimension

Machine learning with tree tensor networks, CP rank constraints, and tensor dropout

Driven-dissipative Bose-Einstein condensation and the upper critical dimension

Criteria for Davies irreducibility of Markovian quantum dynamics

Quantum-classical eigensolver using multiscale entanglement renormalization

Machine learning with tree tensor networks, CP rank constraints, and tensor dropout

Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states

Convergence and quantum advantage of Trotterized MERA for strongly-correlated systems

Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

On the closedness and geometry of tensor network state sets

Tensor Network States with Low-Rank Tensors

Superoperator structures and no-go theorems for dissipative quantum phase transitions

Eigenstate entanglement scaling for critical interacting spin chains

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

Eigenstate Entanglement: Crossover from the Ground State to Volume Laws

Eigenstate entanglement scaling for critical interacting spin chains

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Journal Article Annals of Physics · July 1, 2020 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 netwo ... Full text Cite

Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases

Journal Article Physical Review B · July 1, 2020 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 ch ... Full text Cite

The matrix product approximation for the dynamic cavity method

Journal Article Journal of Statistical Mechanics: Theory and Experiment · January 1, 2020 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, Boo ... Full text Cite

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 Article Physical Review B · December 7, 2018 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 translati ... Full text Cite

Fundamental Limitations for Measurements in Quantum Many-Body Systems

Journal Article Physical Review Letters · August 24, 2018 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 ... Full text Cite

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

Journal Article Physical Review E · January 29, 2018 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 s ... Full text Cite

Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps

Journal Article Physical Review B · November 21, 2017 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 ob ... Full text Cite

One-dimensional quantum systems at finite temperatures can be simulated efficiently on classical computers

Journal Article arXiv:1708.09349 · August 30, 2017 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 te ... Link to item Cite

Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles

Journal Article Physical Review B · May 22, 2017 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 ... Full text Cite

Matrix product purifications for canonical ensembles and quantum number distributions

Journal Article Physical Review B · September 26, 2016 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 ... Full text Cite

Finite-temperature effects on interacting bosonic one-dimensional systems in disordered lattices

Journal Article Physical Review A · March 29, 2016 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 ... Full text Cite

Phase diagram of an extended quantum dimer model on the hexagonal lattice

Journal Article Physical Review Letters · November 18, 2015 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 ... Full text Cite

Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

Journal Article Physical Review B - Condensed Matter and Materials Physics · September 10, 2015 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) ... Full text Cite

Bound states and entanglement in the excited states of quantum spin chains

Journal Article Journal of Statistical Mechanics: Theory and Experiment · October 1, 2014 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 ... Full text Cite

Domain-wall melting in ultracold-boson systems with hole and spin-flip defects

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · June 4, 2014 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 exampl ... Full text Cite

Algebraic versus exponential decoherence in dissipative many-particle systems

Journal Article Physical Review Letters · October 11, 2013 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 ... Full text Cite

Multispinon continua at zero and finite temperature in a near-ideal heisenberg Chain

Journal Article Physical Review Letters · September 26, 2013 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 energ ... Full text Cite

Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes

Journal Article New Journal of Physics · July 1, 2013 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 r ... Full text Cite

Erratum: Dissipative quantum church-turing theorem (Physical Review Letters (2011) 107 (120501))

Journal Article Physical Review Letters · September 13, 2012 Full text Cite

Quasilocality and efficient simulation of Markovian quantum dynamics

Journal Article Physical Review Letters · June 5, 2012 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 o ... Full text Cite

Solving condensed-matter ground-state problems by semidefinite relaxations

Journal Article Physical Review Letters · May 17, 2012 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 b ... Full text Cite

Dissipative quantum Church-Turing theorem

Journal Article Physical Review Letters · September 12, 2011 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 cons ... Full text Cite

Real-space renormalization yields finite correlations

Journal Article Physical Review Letters · July 2, 2010 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, ... Full text Cite

Unitary circuits for strongly correlated fermions

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · May 28, 2010 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 reord ... Full text Cite

Contraction of fermionic operator circuits and the simulation of strongly correlated fermions

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · October 30, 2009 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 t ... Full text Cite

Spectral functions in one-dimensional quantum systems at finite temperature using the density matrix renormalization group

Journal Article Physical Review B - Condensed Matter and Materials Physics · June 1, 2009 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 spe ... Full text Cite

Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · May 1, 2009 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 ... Full text Cite

Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · August 22, 2008 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 presenc ... Full text Cite

Dephasing and the steady state in quantum many-particle systems

Journal Article Physical Review Letters · March 12, 2008 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 suffici ... Full text Cite

Entanglement entropy in collective models

Journal Article Journal of Statistical Mechanics: Theory and Experiment · January 1, 2007 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 div ... Full text Cite

Entanglement and boundary critical phenomena

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · November 27, 2006 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 ... Full text Cite

Entanglement scaling in critical two-dimensional fermionic and bosonic systems

Journal Article Physical Review A - Atomic, Molecular, and Optical Physics · September 20, 2006 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 fermi ... Full text Cite

Entanglement entropy beyond the free case

Journal Article Physical Review Letters · January 1, 2006 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 l ... Full text Cite