Eigenvalue statistics of reduced density matrix during driving and relaxation

TL;DR

This paper investigates the eigenvalue statistics of reduced density matrices in a driven and relaxing one-dimensional correlated metal, revealing universal behaviors and thermal characteristics depending on the system's state.

Contribution

It provides the first numerical analysis of eigenvalue statistics of reduced density matrices during driving and relaxation in correlated metals, highlighting universality and thermalization features.

Findings

Eigenvalue statistics follow Gaussian ensemble universality in driven and equilibrium states.

Spectra of driven subsystems are well described by Gibbs thermal distribution.

Subsystem entropy correlates with time-dependent energy during relaxation.

Abstract

We study a subsystem of an isolated one-dimensional correlated metal when it is driven by a steady electric field or when it relaxes after driving. We obtain numerically exact reduced density matrix $\rho$ for subsystems which are sufficiently large to give significant eigenvalue statistics and spectra of $\log(\rho)$. We show that both for generic as well as for the integrable model the statistics follows the universality of Gaussian unitary and orthogonal ensembles for driven and equilibrium systems, respectively. Moreover, the spectra of modestly driven subsystems are well described by the Gibbs thermal distribution with the entropy determined by the time-dependent energy only.