DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Thermalization at low temperatures via weakly damped multisite baths

Journal Article · · Physical Review. B
ORCiD logo [1]; ORCiD logo [2];  [3]
  1. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
  2. University of Maryland, College Park, MD (United States)
  3. Brandeis University, Waltham, MA (United States)

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

Research Organization:
US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Advanced Scientific Computing Research (ASCR)
Sponsoring Organization:
USDOE
OSTI ID:
2424709
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 108; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (108)

On the generators of quantum dynamical semigroups journal June 1976
Notes on the complex Sachdev-Ye-Kitaev model journal February 2020
A note on the SYK model with complex fermions journal December 2017
Commuting transfer matrices in the chiral Potts models: Solutions of star-triangle equations with genus>1 journal August 1987
Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations journal June 1990
Melting and wetting transitions in the three-state chiral clock model journal September 1983
Quantum model for commensurate-incommensurate transitions journal January 1983
The density-matrix renormalization group in the age of matrix product states journal January 2011
A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal October 2014
Time-evolution methods for matrix-product states journal December 2019
Dualities and the phase diagram of the p -clock model journal January 2012
Quantum states and phases in driven open quantum systems with cold atoms journal September 2008
Ensemble Method in the Theory of Irreversibility journal November 1960
Completely positive dynamical semigroups of N-level systems journal January 1976
Quantum trajectories and open many-body quantum systems journal March 2014
Minimal length scales for the existence of local temperature journal March 2006
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems journal March 2008
Third quantization: a general method to solve master equations for quadratic open Fermi systems journal April 2008
Markovian master equations: a critical study journal November 2010
Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain journal February 2010
Matrix product simulations of non-equilibrium steady states of quantum spin chains journal February 2009
Spectral theorem for the Lindblad equation for quadratic open fermionic systems journal July 2010
Transport in a one-dimensional isotropic Heisenberg model at high temperature journal December 2011
Parafermionic edge zero modes in Z n -invariant spin chains journal November 2012
Heat transport in the X X Z spin chain: from ballistic to diffusive regimes and dephasing enhancement journal July 2013
Hand-waving and interpretive dance: an introductory course on tensor networks journal May 2017
Quantum Physics in One Dimension book December 2003
Product spectrum ansatz and the simplicity of thermal states journal September 2019
Open-system tensor networks and Kramers' crossover for quantum transport journal May 2020
Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths journal March 2022
Searching for Lindbladians obeying local conservation laws and showing thermalization journal June 2023
Local temperature in quantum thermal states journal May 2009
Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays journal August 2015
Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings journal February 2016
Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results journal June 2016
Numerical study of the chiral Z 3 quantum phase transition in one spatial dimension journal August 2018
Many-body open quantum systems beyond Lindblad master equations journal January 2019
Excitation spectra of quantum matter without quasiparticles. I. Sachdev-Ye-Kitaev models journal February 2021
Excitation spectra of quantum matter without quasiparticles. II. Random t − J models journal February 2021
Temperature-dependent energy diffusion in chaotic spin chains journal March 2021
Near-equilibrium approach to transport in complex Sachdev-Ye-Kitaev models journal June 2022
Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach journal May 2023
Incommensurate and commensurate phases in asymmetric clock models journal July 1981
Simple three-state model with infinitely many phases journal November 1981
Phase diagrams of surface structures from Bethe-ansatz solutions of the quantum sine-Gordon model journal September 1983
Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures journal April 1998
Non-Fermi-liquid regime of a doped Mott insulator journal February 1999
Quantum fluctuations of a nearly critical Heisenberg spin glass journal March 2001
Diffusive high-temperature transport in the one-dimensional Hubbard model journal September 2012
Magnetization transport in spin ladders and next-nearest-neighbor chains journal November 2013
Phase diagram of the Z 3 parafermionic chain with chiral interactions journal July 2015
Influence of dephasing on many-body localization journal March 2016
Numerical study of fermion and boson models with infinite-range random interactions journal July 2016
Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model journal January 2017
Finite coupling effects in double quantum dots near equilibrium journal January 2017
Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography journal April 2017
Thermalization in open quantum systems journal April 2018
Quantum field theory for the chiral clock transition in one spatial dimension journal November 2018
Asymmetry in energy versus spin transport in certain interacting disordered systems journal March 2019
Constructing neural stationary states for open quantum many-body systems journal June 2019
Thermalization with detailed-balanced two-site Lindblad dissipators journal August 2019
Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation journal April 2020
Modeling heat transport through completely positive maps journal September 2007
Thermalization and ergodicity in one-dimensional many-body open quantum systems journal May 2010
Coexistence of energy diffusion and local thermalization in nonequilibrium X X Z spin chains with integrability breaking journal April 2015
Relaxation times of dissipative many-body quantum systems journal October 2015
Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems journal July 2010
Open X X Z Spin Chain: Nonequilibrium Steady State and a Strict Bound on Ballistic Transport journal May 2011
Spin Transport in a One-Dimensional Anisotropic Heisenberg Model journal May 2011
Exact Nonequilibrium Steady State of a Strongly Driven Open X X Z Chain journal September 2011
Exact Matrix Product Solution for the Boundary-Driven Lindblad X X Z Chain journal January 2013
Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder journal February 2013
Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems journal October 2013
Exact Nonequilibrium Steady State of an Open Hubbard Chain journal January 2014
Variational Principle for Steady States of Dissipative Quantum Many-Body Systems journal January 2015
Infinitely Dimensional Lax Structure for the One-Dimensional Hubbard Model journal March 2015
Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems journal June 2015
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems journal June 2016
Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems journal June 2019
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics journal June 2019
Variational Neural-Network Ansatz for Steady States in Open Quantum Systems journal June 2019
Breaking the Entanglement Barrier: Tensor Network Simulation of Quantum Transport journal March 2020
Exact Nonequilibrium Steady State of Open XXZ/XYZ Spin- 1/2 Chain with Dirichlet Boundary Conditions journal April 2020
Emergent Hydrodynamics in Nonequilibrium Quantum Systems journal July 2020
Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks journal December 2021
Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation journal February 2022
Domain Walls and the Melting of Commensurate Surface Phases journal September 1982
Gapless spin-fluid ground state in a random quantum Heisenberg magnet journal May 1993
Mean Field Theory of a Quantum Heisenberg Spin Glass journal July 2000
Efficient Classical Simulation of Slightly Entangled Quantum Computations journal October 2003
Efficient Simulation of One-Dimensional Quantum Many-Body Systems journal July 2004
Existence of Temperature on the Nanoscale journal August 2004
Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems journal November 2004
Mixed-State Dynamics in One-Dimensional Quantum Lattice Systems: A Time-Dependent Superoperator Renormalization Algorithm journal November 2004
Universal Relaxational Dynamics of Gapped One-Dimensional Models in the Quantum Sine-Gordon Universality Class journal October 2005
Energy transport in Sachdev-Ye-Kitaev networks coupled to thermal baths journal April 2022
Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines journal August 2020
Locality of Temperature journal July 2014
Bekenstein-Hawking Entropy and Strange Metals journal November 2015
Simulation methods for open quantum many-body systems journal March 2021
Finite-temperature transport in one-dimensional quantum lattice models journal May 2021
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems journal December 2021
Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids journal September 2022
Nonequilibrium boundary-driven quantum systems: Models, methods, and properties journal December 2022
On Quantum Theory of Transport Phenomena: Steady Diffusion journal December 1958
The local approach to quantum transport may violate the second law of thermodynamics journal July 2014
Intensive temperature and quantum correlations for refined quantum measurements journal April 2012
Measurable consequences of the local breakdown of the concept of temperature journal June 2005