Subsystem ETH

TL;DR

This paper introduces a refined form of the Eigenstate Thermalization Hypothesis (ETH), called subsystem ETH, which focuses on the reduced density matrices of subsystems in chaotic quantum systems, supported by numerical evidence.

Contribution

It proposes a new formulation of ETH based on subsystems, detailing its implications and providing numerical validation in a 1D Ising spin-chain.

Findings

Subsystem ETH guarantees thermalization for certain observables within subsystems.

The paper calculates volume-proportional contributions to entanglement entropies.

Numerical evidence supports the validity of subsystem ETH in a 1D Ising model.

Abstract

Motivated by the qualitative picture of Canonical Typicality, we propose a refined formulation of the Eigenstate Thermalization Hypothesis (ETH) for chaotic quantum systems. The new 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.