Eigenstate thermalization from the clustering property of correlation
arXiv:1905.01886 · doi:10.1103/PhysRevLett.124.200604
Abstract
The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in non-critical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting the clustering property. We investigate two regimes, namely, regimes of high and low density of states corresponding to high and low energy regimes, respectively. We show that the clustering property is connected to several properties on the eigenstate thermalization through the density of states. Remarkably, the eigenstate thermalization is obtained in the low-energy regime with sparse density of states, which is typically seen in gapped systems. For the high-energy regime, we demonstrate the ensemble equivalence between microcanonical and canonical ensembles even for subexponentially small energy shell with respect to the system size, which eventually leads to the weak version of eigenstate thermalization.
arXiv comment6 pages + 11 pages, 7 figures
References in corpus (46)
- Chaos and Quantum Thermalization
- Many body localization and thermalization in quantum statistical mechanics
- 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
- Quantum thermalization through entanglement in an isolated many-body system
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum many-body scars
- The role of quantum information in thermodynamics --- a topical review
- Quantum Quench in the Transverse Field Ising Chain
- Spectral Gap and Exponential Decay of Correlations
- Eigenstate Thermalization Hypothesis
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
- Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
- Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
- Density-Matrix Spectra of Solvable Fermionic Systems
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Thermalization near integrability in a dipolar quantum Newton's cradle
- Critical thermalization of a disordered dipolar spin system in diamond
- Entropy and Entanglement in Quantum Ground States
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- Locality of temperature
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- An area law for the entropy of low-energy states
- Fluctuation Theorem for Many-Body Pure Quantum States
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
- Ensemble equivalence for general many-body systems
- Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems
- Some Properties of Correlations of Quantum Lattice Systems in Thermal Equilibrium
- On the local equivalence between the canonical and the microcanonical distributions for quantum spin systems
- Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
- Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interaction
- Entanglement area law from specific heat capacity
- Locality of temperature in spin chains
- Quantum Macrostates, Equivalence of Ensembles and an H-Theorem
- Connecting probability distributions of different operators and generalization of the Chernoff-Hoeffding inequality
- Cluster expansions and correlation functions
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- Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis
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