Entanglement-ergodic quantum systems equilibrate exponentially well
arXiv:1802.02052 · doi:10.1103/PhysRevLett.123.200604
Abstract
One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels. But results not referring to typicality which show that natural initial states actually fulfill this condition are lacking. In this work, we present stringent results for equilibration for systems in which Renyi entanglement entropies in energy eigenstates with finite energy density are extensive for at least some, not necessarily connected, sub-system. Our results reverse the logic of common arguments, in that we derive equilibration from a weak condition akin to the eigenstate thermalization hypothesis, which is usually attributed to thermalization in systems that are assumed to equilibrate in the first place. We put the findings into the context of studies of many-body localization and many-body scars.
arXiv comment6+8 pages; v3: improved presentation, close to published version
References in corpus (74)
- Many-Body Physics with Ultracold Gases
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Concentrating Partial Entanglement by Local Operations
- Area laws for the entanglement entropy - a review
- Nonequilibrium dynamics of closed interacting quantum systems
- Probing many-body dynamics on a 51-atom quantum simulator
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- 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
- Average Entropy of a Subsystem
- Quantum many-body systems out of equilibrium
- Time-dependence of correlation functions following a quantum quench
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum many-body scars
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Area laws in quantum systems: mutual information and correlations
- Quantum Quench in the Transverse Field Ising Chain
- Quantum mechanical evolution towards thermal equilibrium
- Time evolution of local observables after quenching to an integrable model
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Area laws in a many-body localized state and its implications for topological order
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Dephasing and the steady state in quantum many-particle systems
- Emergent SU(2) dynamics and perfect quantum many-body scars
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Semiclassical Foundation of Universality in Quantum Chaos
- Exact Excited States of Non-Integrable Models
- Remarks on the notion of quantum integrability
- Does a single eigenstate encode the full Hamiltonian?
- Quantum equilibration in finite time
- Equilibration of quantum systems and subsystems
- Emergence of coherence and the dynamics of quantum phase transitions
- Evolution of entanglement after a local quench
- Quantum quenches in the many-body localized phase
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Many-body quantum chaos: Analytic connection to random matrix theory
- Exploring local quantum many-body relaxation by atoms in optical superlattices
- Typical fast thermalization processes in closed many-body systems
- Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
- Locality of temperature
- Statistical distribution of quantum entanglement for a random bipartite state
- Many-body localisation implies that eigenvectors are matrix-product states
- Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
- Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
- Equilibration of isolated macroscopic quantum systems
- Normal Typicality and von Neumann's Quantum Ergodic Theorem
- The spectral gap for some spin chains with discrete symmetry breaking
- Probing local relaxation of cold atoms in optical superlattices
- Universality in volume law entanglement of pure quantum states
- Statistical properties of the spectrum the extended Bose-Hubbard model
- Entanglement rates and area laws
- On the time scales in the approach to equilibrium of macroscopic quantum systems
- Renyi Entropy of Chaotic Eigenstates
- Quantum Systems Equilibrate Rapidly for Most Observables
- Spectra and eigenstates of spin chain Hamiltonians
- Equilibration time scales of physically relevant observables
- Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace
- The complexity of energy eigenstates as a mechanism for equilibration
- Total correlations of the diagonal ensemble herald the many-body localization transition
- Universal eigenstate entanglement of chaotic local Hamiltonians
- Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems
- Equilibration time scales in closed many-body quantum systems
- Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
- Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems
- Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
- Towards local equilibration in closed interacting quantum many-body systems
- What it takes to shun equilibration
- Equilibration of Quantum Gases
Cited by in corpus (40)
- Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
- Entanglement growth in diffusive systems
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- Bounds in Nonequilibrium Quantum Dynamics
- Revivals imply quantum many-body scars
- Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
- Sample complexity of device-independently certified "quantum supremacy"
- Quantum many-body scars in transverse field Ising ladders and beyond
- Temporal Entanglement in Chaotic Quantum Circuits
- Classicality, Markovianity and local detailed balance from pure state dynamics
- Emergent statistical mechanics from properties of disordered random matrix product states
- Entanglement transitions as a probe of quasiparticles and quantum thermalization
- Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
- Fluctuations of subsystem entropies at late times
- Equilibration on average in quantum processes with finite temporal resolution
- Disorder enhanced quantum many-body scars in Hilbert crystals
- Quantum and Classical Dynamics with Random Permutation Circuits
- Finite-size scaling analysis of eigenstate thermalization
- Instability of localization in translation-invariant systems
- Extensive entropy from unitary evolution
- Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
- Non-equilibration, synchronization, and time crystals in isotropic Heisenberg models
- Matrix product state approximations to quantum states of low energy variance
- Concentration of quantum equilibration and an estimate of the recurrence time
- Typical thermalization of low-entanglement states
- Reviving product states in the disordered Heisenberg chain
- The second law of thermodynamics from concavity of energy eigenvalues
- Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
- Equilibration of Isolated Systems: investigating the role of coarse-graining on the initial state magnetization
- Estimate of equilibration times of quantum correlation functions in the thermodynamic limit based on Lanczos coefficients
- Optimisation of ultrafast singlet fission in 1D rings towards unit efficiency
- Probing thermalization in quenched (non-)integrable Fermi-Hubbard models
- Quantized and maximum entanglement from sublattice symmetry
- Sampling and the complexity of nature
- Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations
- Long-time properties of generic Floquet systems are approximately periodic with the driving period
- The second law of thermodynamics from concave energy in classical mechanics
- Equilibration of Non-interacting Photons and Quantum Signatures of Chaos
- Observation of hierarchy of Hilbert space ergodicities in the quantum dynamics of a single spin
- Volume-law entanglement entropy of typical pure quantum states