Eigenstate thermalization from the clustering property of correlation

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.

6 pages + 11 pages, 7 figures

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• Quantum many-body systems in thermal equilibrium
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• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• Learning quantum many-body systems from a few copies
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Double-bracket quantum algorithms for diagonalization
• Refining Deutsch's approach to thermalization
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Thermalization of locally perturbed many-body quantum systems
• Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations
• Thermal Area Law in Long-Range Interacting Systems
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Clustering theorem in 1D long-range interacting systems at arbitrary temperatures
• Limitations of variational quantum algorithms: a quantum optimal transport approach
• Typical thermalization of low-entanglement states
• Subsystem eigenstate thermalization hypothesis for translation invariant systems
• Allosteric impurity effects in long spin chains
• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Temperature and conditions for thermalization after canonical quenches
• Integral fluctuation theorems and trace-preserving map
• Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis
• Basis dependence of eigenstate thermalization
• Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis