Subsystem eigenstate thermalization hypothesis

2015/11/30 by Anatoly Dymarsky, Hong Liu, Nima Lashkari · 9 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Density matrix #Eigenvalues and eigenvectors #Epistemology #Phenomenology (philosophy) #Philosophy #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Set (abstract data type) #Statistical physics #Theoretical physics #Thermalisation #cond-mat.stat-mech #hep-th #quant-ph

paper · pdf · doi:10.1103/physreve.97.012140

published as Phys. Rev. E 97, 012140 (2018) · Expanded version replacing earlier arXiv:1511.06680

openalex publication_date 2018/01/25 · arxiv created 2018/04/05 · arxiv updated 2018/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Motivated by the qualitative picture of canonical typicality, we propose a refined formulation of the eigenstate thermalization hypothesis (ETH) for chaotic quantum systems. This formulation, which we refer to as subsystem ETH, is in terms of the reduced density matrix of subsystems. This strong form of ETH outlines the set of observables defined within the subsystem for which it guarantees eigenstate thermalization. We discuss the limits when the size of the subsystem is small or comparable to its complement. In the latter case we outline the way to calculate the leading volume-proportional contribution to the von Neumann and Renyi entanglment entropies. Finally, we provide numerical evidence for the proposal in the case of a one-dimensional Ising spin chain.

Citations

• From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
• The approach to thermal equilibrium in quantized chaotic systems
• Approach to thermal equilibrium of macroscopic quantum systems
• Chaos and Quantum Thermalization
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• Quantum statistical mechanics in a closed system
• Thermodynamic entropy of a many-body energy eigenstate

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• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Quantum chaos, equilibration, and control in extremely short spin chains
• Experimental realization of the classical Dicke model
• Eigenstate thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
• Holographic Rényi Entropy at High Energy Density
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models