Hydrodynamics and the eigenstate thermalization hypothesis

TL;DR

This paper links the behavior of ETH matrix elements to hydrodynamic decay of autocorrelations, supported by numerical simulations of non-integrable spin models, advancing understanding of thermalization in quantum systems.

Contribution

It establishes a novel relation between ETH matrix element behavior and hydrodynamics, supported by numerical evidence in non-integrable spin models.

Findings

Off-diagonal ETH singularity relates to autocorrelation decay

Hydrodynamics constrains ETH profile in energy space

Numerical simulations confirm theoretical predictions

Abstract

The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the off-diagonal part of ETH at small energy differences, and (ii) the smooth profile of the diagonal part of ETH as a function of the energy density. We establish this connection from the decay of the autocorrelation functions of local operators, which is constrained by the presence of local conserved quantities whose evolution is described by hydrodynamics. We corroborate our predictions with numerical simulations of two non-integrable spin-1 Ising models, one diffusive and one super-diffusive, which we perform using dynamical quantum typicality up to 18 spins.