Necessity of Eigenstate Thermalization

Abstract

Under the Eigenstate Thermalization Hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only sufficient but also necessary for thermalization. More specifically, we consider systems coupled to baths with well-defined macroscopic temperature and show that whenever all product states thermalize then the ETH must hold. Our result definitively settles the question of determining whether a quantum system has a thermal behaviour, reducing it to checking whether its Hamiltonian satisfies the ETH.

7 pages, misprint corrected in Eqs. (A14), (A15)

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Many-body localization in periodically driven systems
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
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Cited by in corpus (38)

• Eigenstate Thermalization Hypothesis
• Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Bound on Eigenstate Thermalization from Transport
• Bounds in Nonequilibrium Quantum Dynamics
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Thermalization without eigenstate thermalization hypothesis after a quantum quench
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Atypicality of Most Few-Body Observables
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Dynamical typicality approach to eigenstate thermalization
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Universal locality of quantum thermal susceptibility
• Partial breakdown of quantum thermalization in a Hubbard-like model
• Quantum concentration inequalities
• Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
• Localized Mode and Nonergodicity of a Harmonic Oscillator Chain
• Reply to "Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"" by Mondaini et.al
• Information Scrambling with Conservation Laws
• Necessity of eigenstate thermalization for equilibration towards unique expectation values when starting from generic initial states
• Generalized eigenstate typicality in translation-invariant quasifree fermionic models
• Speed limit for open systems coupled to general environments
• Analytic model of thermalization: Quantum emulation of classical cellular automata
• Assigning Temperatures to Eigenstates
• Classical route to ergodicity and scarring in collective quantum systems
• Scaling at the OTOC Wavefront: free versus chaotic models
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Observing quantum many-body scars in random quantum circuits
• Open-system eigenstate thermalization in a noninteracting integrable model
• Hidden quasi-local charges and Gibbs ensemble in a Lindblad system
• Key Observable for Linear Thermalization
• Typical pure nonequilibrium steady states and irreversibility for quantum transports
• Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
• Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems
• On the difference between thermalization in open and isolated quantum systems: a case study
• Does the Eigenstate Thermalization Hypothesis Imply Thermalization?
• Theoretical study on thermalization in isolated quantum systems