Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

TL;DR

This paper investigates how the decay rate of long-range hopping in disordered one-dimensional fermionic systems influences localization and thermalization, revealing a universal power-law relaxation behavior in certain regimes.

Contribution

It introduces a model showing how decay rates affect localization and thermalization, uncovering a new universality class with power-law relaxation in disordered quantum systems.

Findings

Fast decay promotes localization and prevents thermalization.

Slower decay allows thermalization with a power-law approach.

Identifies a new universality class with power-law relaxation.

Abstract

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.