Tensor-network method to simulate strongly interacting quantum thermal machines

Abstract

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at fixed temperature and chemical potential. Our method works at finite temperature, beyond linear response and weak system-reservoir coupling, and allows for non-quadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped towards thermal equilibrium, in order to represent continuum baths and a novel tensor network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with non-quadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the super-diffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at finite temperature and its connection to charge conjugation-parity, going beyond the predictions of single-site boundary driving configurations.

arXiv comment21 figures, 25 pages. Updated results, content and references. Journal version (Feature in APS Physics)

References in corpus (80)

• The density-matrix renormalization group in the age of matrix product states
• The numerical renormalization group method for quantum impurity systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The role of quantum information in thermodynamics --- a topical review
• A single-atom heat engine
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Quantum heat engines and refrigerators: Continuous devices
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Efficient simulation of strong system-environment interactions
• Experimental demonstration of quantum effects in the operation of microscopic heat engines
• Spin transport in a one-dimensional anisotropic Heisenberg model
• A quantum-dot heat engine operating close to the thermodynamic efficiency limits
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Markovian master equations for quantum thermal machines: local vs global approach
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Reconciliation of quantum local master equations with thermodynamics
• Quantum absorption refrigerator with trapped ions
• Families of quasi-local conservation laws and quantum spin transport
• Tunable photonic heat transport in a quantum heat valve
• A spin heat engine coupled to a harmonic-oscillator flywheel
• Modeling heat transport through completely positive maps
• Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems
• Nonequilibrium Green's function method for quantum thermal transport
• Thermoelectric efficiency at maximum power in low-dimensional systems
• Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
• Squeezed thermal reservoirs as a resource for a nano-mechanical engine beyond the Carnot limit
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Efficient simulation of finite-temperature open quantum systems
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Performance of a quantum heat engine at strong reservoir coupling
• The thermodynamic cost of driving quantum systems by their boundaries
• Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
• Variational matrix product state approach to quantum impurity models
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Matrix product solutions of boundary driven quantum chains
• Out of equilibrium open quantum systems: a comparison of approximate Quantum Master Equation approaches with exact results
• Auxiliary master equation approach to non-equilibrium correlated impurities
• Non-additive dissipation in open quantum networks out of equilibrium
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Dephasing-induced diffusive transport in anisotropic Heisenberg model
• Single atom energy-conversion device with a quantum load
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
• Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
• Dissipation-assisted matrix product factorization
• Heat transport in the $XXZ$ spin chain: from ballistic to diffusive regimes and dephasing enhancement
• A renormalization group approach to time dependent transport through correlated quantum dots
• The Accuracy of Perturbative Master Equations
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs
• Breaking the entanglement barrier: Tensor network simulation of quantum transport
• High-temperature coherent transport in the XXZ chain in the presence of an impurity
• Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
• Thermodynamic deficiencies of some simple Lindblad operators
• Transport in a one-dimensional isotropic Heisenberg model at high temperature
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Non-equilibrium quantum chains under multi-site Lindblad baths
• The Tensor Network Theory Library
• Landauer's formula with finite-time relaxation: Kramers' crossover in electronic transport
• Manipulating energy and spin currents in nonequilibrium systems of interacting qubits
• Master Equations for Electron Transport: The Limits of the Markovian Limit
• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Markovian Treatment of non-Markovian Dynamics of Open Fermionic Systems
• Dephasing enhanced spin transport in the ergodic phase of a many-body localizable system
• Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Thermalization in Open Quantum Systems
• Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking
• Nonequilibrium mesoscopic Fermi reservoirs distributions and particle current through a coherent quantum system
• Transport Through a Correlated Interface: Auxiliary Master Equation Approach
• Classifying transport behavior via current fluctuations in open quantum systems
• Ultra-fast control of magnetic relaxation in a periodically driven Hubbard model
• Transport enhancement from incoherent coupling between one-dimensional quantum conductors

Cited by in corpus (59)

• Finite-temperature transport in one-dimensional quantum lattice models
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Periodically refreshed baths to simulate open quantum many-body dynamics
• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
• Using the Environment to Understand non-Markovian Open Quantum Systems
• Strong coupling effects in quantum thermal transport with the reaction coordinate method
• Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
• Sublinear scaling in non-Markovian open quantum systems simulations
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Rényi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems
• Quantum dynamics in the interacting Fibonacci chain
• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• Quasi-Lindblad pseudomode theory for open quantum systems
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Finite-time Landauer principle beyond weak coupling
• Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
• Improved Efficiency of Open Quantum System Simulations Using Matrix Products States in the Interaction Picture
• Invasiveness of non-equilibrium quantum thermometry
• Entropy and information flow in quantum systems strongly coupled to baths
• Thermodynamics of a continuously monitored double quantum dot heat engine in the repeated interactions framework
• Particle current statistics in driven mesoscale conductors
• Analytic expressions for the steady-state current with finite extended reservoirs
• Thermodynamic performance of a periodically driven harmonic oscillator correlated with the baths
• Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach
• The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Dynamics of a quantum system interacting with white non-Gaussian baths: Poisson noise master equation
• Strongly coupled quantum Otto cycle with single qubit bath
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Waiting-times statistics in boundary driven free fermion chains
• Giant rectification in strongly-interacting driven tilted systems
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Efficient construction of tensor-network representations of many-body Gaussian states
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Powering an autonomous clock with quantum electromechanics
• Optimal qubit-mediated quantum heat transfer via noncommuting operators and strong coupling effects
• Dephasing-assisted transport in a tight-binding chain with a linear potential
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Nonequilibrium steady states in multi-bath quantum collision models
• Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction coordinate approach
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Approaching the scaling limit of transport through lattices with dephasing
• Dephasing enhanced transport in boundary-driven quasiperiodic chains
• Exact description of fermionic reservoirs via purified damped ancillary fermions
• Subtleties in the pseudomodes formalism
• Dual current anomalies and quantum transport within extended reservoir simulations
• Purified pseudomode model for nonlinear system-bath interactions