Nonequilibrium localization and the interplay between disorder and interactions

TL;DR

This paper investigates how disorder and interactions influence localization in quantum systems, revealing a complex interplay that affects dynamical behavior and delocalization phenomena through numerical and analytical methods.

Contribution

It introduces the concept of dynamical state-space localization via Loschmidt echo and connects real-space and state-space localization, highlighting their interplay in non-equilibrium quantum systems.

Findings

In noninteracting systems, the average echo increases with disorder, inversely related to localization length.

In interacting systems, the equilibration length scale is bounded and decreases with higher average echo.

Disorder and interactions together cause non-monotonic echo behavior, indicating a complex interplay leading to delocalization.

Abstract

We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localization are independent concepts in general, we show that both perspectives may be directly connected through a specific choice of initial states, namely, maximally localized states (ML-states). We show numerically that in the noninteracting case the average echo is found to be monotonically increasing with increasing disorder; these results are in agreement with an analytical evaluation in the single particle case in which the echo is found to be inversely proportional to the localization length. We also show that for interacting systems, the length scale under which equilibration may occur is upper bounded and such bound is smaller the greater the average echo of ML-states. When disorder and interactions, both being localization mechanisms, are simultaneously at play the echo features a non-monotonic behaviour indicating a non-trivial interplay of the two processes. This interplay induces delocalization of the dynamics which is accompanied by delocalization in real-space. This non-monotonic behaviour is also present in the effective integrability which we show by evaluating the gap statistics.