Time-dependent generalized Gibbs ensembles in open quantum systems

Abstract

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

arXiv comment10 pages, 8 figures

References in corpus (55)

• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• An Open-System Quantum Simulator with Trapped Ions
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Observation of Entangled States of a Fully Controlled 20-Qubit System
• Quasilocal charges in integrable lattice systems
• Reduced Density Matrix after a Quantum Quench
• Effective operator formalism for open quantum systems
• Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
• Prethermalization and thermalization in models with weak integrability breaking
• Solvable Hydrodynamics of Quantum Integrable Systems
• Prethermalization and universal dynamics in near-integrable quantum systems
• The Quench Action
• Pre-thermalization in a non-integrable quantum spin chain after a quench
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• Hydrodynamic long-time tails after a quantum quench
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Generalized Gibbs Ensemble for Heisenberg Spin Chains
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Thermalization and light cones in a model with weak integrability breaking
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Relaxation, pre-thermalization and diffusion in a noisy Quantum Ising Chain
• Quantum thermalization dynamics with Matrix-Product States
• The Floquet-Boltzmann equation
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions
• Spin conductivity in almost integrable spin chains
• Quantum Quenches in the Luttinger model and its close relatives
• Pre-relaxation in weakly interacting models
• Pumping approximately integrable systems
• Local and Quasilocal Conserved Quantities in Integrable Systems
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Prethermalization and Thermalization of a Quenched Interacting Luttinger Liquid
• Derivation of Transport Equations using the Time-Dependent Projection Operator Method
• Thermalization rates in the one dimensional Hubbard model with next-to-nearest neighbor hopping
• The Structure of Conserved Charges in Open Spin Chains

Cited by in corpus (59)

• Finite-temperature transport in one-dimensional quantum lattice models
• Hydrodynamic Diffusion in Integrable Systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Prethermalization and Thermalization in Isolated Quantum Systems
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Constructing Integrable Lindblad Superoperators
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Strong correlations in lossy one-dimensional quantum gases: from the quantum Zeno effect to the generalized Gibbs ensemble
• Universality in driven open quantum matter
• Correlation engineering via non-local dissipation
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Integrability-protected adiabatic reversibility in quantum spin chains
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Entangled multiplets and unusual spreading of quantum correlations in a continuously monitored tight-binding chain
• Activating many-body localization in solids by driving with light
• Exploring nonequilibrium phases of photo-doped Mott insulators with Generalized Gibbs ensembles
• The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement
• Reaction-limited quantum reaction-diffusion dynamics
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• A dynamical theory for one-dimensional fermions with strong two-body losses: universal non-Hermitian Zeno physics and spin-charge separation
• Many-Body Open Quantum Systems
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Photo-induced nonequilibrium states in Mott insulators
• Driven-dissipative Ising Model: An exact field-theoretical analysis
• One-dimensional spin-1/2 fermionic gases with two-body losses: weak dissipation and spin conservation
• Dicke transition in open many-body systems determined by fluctuation effects
• Rectification in Nonequilibrium Steady States of Open Many-Body Systems
• Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
• Engineering generalized Gibbs ensembles with trapped ions
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• From observations to complexity of quantum states via unsupervised learning
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Quantum reaction-limited reaction-diffusion dynamics of annihilation processes
• Effects of atom losses on a one-dimensional lattice gas of hardcore bosons
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Pre-thermalization in a classical phonon field: slow relaxation of the number of phonons
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Multiple relaxation times in perturbed XXZ chain
• Long-living prethermalization in nearly integrable spin ladders
• Fluctuation-Induced Bistability of Fermionic Atoms Coupled to a Dissipative Cavity
• Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• Tensor-network approach to thermalization in open quantum many-body systems
• Back-reaction and correlation effects on pre-thermalization in Mott-Hubbard systems
• Prethermalization with negative specific heat
• Prethermalization of quantum systems interacting with non-equilibrium environments
• Accuracy of time-dependent GGE under weak dissipation
• Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
• Kinetics of Quantum Reaction-Diffusion systems
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Signatures of Quantum Phase Transitions in Driven Dissipative Spin Chains
• Gibbs state sampling via cluster expansions
• Bistabilities and domain walls in weakly open quantum systems