Subsystem eigenstate thermalization hypothesis.
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TLDR
A refined formulation of the eigenstate thermalization hypothesis (ETH) for chaotic quantum systems is proposed in terms of the reduced density matrix of subsystems, which outlines the set of observables defined within the subsystem for which it guarantees eigen state thermalization.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 chainread more
Citations
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Eigenstate thermalization hypothesis.
TL;DR: The eigenstate thermalization hypothesis (ETH) as discussed by the authors has been used extensively by both analytic and numerical means, and applied to a number of physical situations ranging from black hole physics to condensed matter systems.
Journal ArticleDOI
Universality in volume-law entanglement of scrambled pure quantum states.
TL;DR: A formula for the entanglement entropy of a class of thermal-like states is found and applied more broadly to identify equilibrating states and is exploited as diagnostics for chaotic systems.
Journal ArticleDOI
Entanglement and matrix elements of observables in interacting integrable systems
TL;DR: In this article, the bipartite von Neumann entanglement entropy and matrix elements of local operators in the eigenstates of an interacting integrable Hamiltonian (the paradigmatic spin-1/2 XXZ chain), and contrast their behavior with that of quantum chaotic systems.
Journal ArticleDOI
Structure of chaotic eigenstates and their entanglement entropy.
Chaitanya Murthy,Mark Srednicki +1 more
TL;DR: A chaotic many-body system that is split into two subsystems, with an interaction along their mutual boundary, is considered, and a universal correction to the entanglement entropy is found that is proportional to the square root of the system's heat capacity.
Journal ArticleDOI
Eigenstate entanglement in the Sachdev-Ye-Kitaev model
Yichen Huang,Yingfei Gu +1 more
TL;DR: In this paper, the authors studied the entanglement entropy of eigenstates of the Sachdev-Ye-Kitaev model and proposed a volume law whose coefficient can be calculated analytically from the density of states.
References
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Chaos and quantum thermalization
TL;DR: It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.
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Thermalization and its mechanism for generic isolated quantum systems
TL;DR: It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.
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Quantum statistical mechanics in a closed system
TL;DR: A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution, so by adding a finite but very small perturbation in the form of a random matrix, the results of quantum statistical mechanics are recovered.
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From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
TL;DR: The eigenstate thermalization hypothesis (ETH) as discussed by the authors is a natural extension of quantum chaos and random matrix theory (RMT) that allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath.
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Entanglement and the foundations of statistical mechanics
TL;DR: In this paper, the authors argue that the main postulate of statistical mechanics, the equal a priori probability postulate, should be abandoned as misleading and unnecessary, and they argue that it should be replaced by a general canonical principle, whose physical content is fundamentally different from the postulate it replaces: it refers to individual states, rather than to ensemble or time averages.