From eigenstate thermalization to hydrodynamic transport in correlated metals

TL;DR

This paper introduces a new theoretical framework to compute low-frequency transport properties in strongly correlated, ergodic systems, capturing hydrodynamic effects and relating charge and thermal transport coefficients, validated by numerical studies.

Contribution

It proposes a novel approach based on thermal domains and weak coupling to analyze transport, including non-analytic corrections and a generalized Wiedemann-Franz law.

Findings

Framework captures hydrodynamic long time tails.

Results verified with exact diagonalization.

Establishes a generalized relation between charge and thermal transport.

Abstract

We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency $\omega$, domains of size $\xi \sim\sqrt{D/\omega}$ can be considered as internally thermal, but weakly coupled with each other. We calculate the transport coefficients to lowest order in the coupling, assuming incoherent transport between such domains. Our framework naturally captures the sub-leading non analytic corrections to the transport coefficients, known as hydrodynamic long time tails. In addition, it allows us to obtain a generalized relation between charge and thermal transport coefficients, in the spirit of the Wiedemann-Franz law. We verify our results, which satisfy several non-trivial consistency checks, via exact diagonalization studies on the one-dimensional extended Fermi-Hubbard model.