Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

TL;DR

This paper investigates how a sudden removal of a static force affects the dynamics, thermalization, and transport properties in a disordered one-dimensional fermionic system, revealing universal behavior and conditions for diffusion.

Contribution

It demonstrates a universal correlation function governing post-removal dynamics across phases and links thermalization to eigenstate properties, advancing understanding of non-equilibrium behavior in disordered systems.

Findings

Universality of dynamics independent of initial states and phases.

Eigenstate thermalization hypothesis is necessary and sufficient for thermalization.

Normal diffusion persists under weak disorder, with possible anomalous diffusion at stronger disorder.

Abstract

We study the real-time dynamics of local occupation numbers in a one-dimensional model of spinless fermions with a random on-site potential for a certain class of initial states. The latter are thermal (mixed or pure) states of the model in the presence of an additional static force, but become non-equilibrium states after a sudden removal of this static force. For this class and high temperatures, we show that the induced dynamics is given by a single correlation function at equilibrium, independent of the initial expectation values being prepared close to equilibrium (by a weak static force) or far away from equilibrium (by a strong static force). Remarkably, this type of universality holds true in both, the ergodic phase and the many-body localized regime. Moreover, it does not depend on the specific choice of a unit cell for the local density. We particularly discuss two important consequences. First, the long-time expectation value of the local density is uniquely determined by the fluctuations of its diagonal matrix elements in the energy eigenbasis. Thus, the validity of the eigenstate thermalization hypothesis is not only a sufficient but also a necessary condition for thermalization. Second, the real-time broadening of density profiles is always given by the current autocorrelation function at equilibrium via a generalized Einstein relation. In the context of transport, we discuss the influence of disorder for large particle-particle interactions, where normal diffusion is known to occur in the disorder-free case. Our results suggest that normal diffusion is stable against weak disorder, while they are consistent with anomalous diffusion for stronger disorder below the localization transition. Particularly, for weak disorder, Gaussian density profiles can be observed for single disorder realizations, which we demonstrate for finite lattices up to 31 sites.