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.

Document Type

Article

Publication Date

1-25-2018

Notes/Citation Information

Published in Physical Review E, v. 97, issue 1, 012140, p. 1-7.

©2018 American Physical Society

The copyright holder has granted permission for posting the article here.

Digital Object Identifier (DOI)

https://doi.org/10.1103/PhysRevE.97.012140

Funding Information

This work was supported by funds provided by MIT-Skoltech Initiative.

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