Interaction-disorder competition in a spin system evaluated through the Loschmidt Echo

TL;DR

This paper investigates how interactions and disorder influence thermalization in quantum spin systems using the Loschmidt echo, revealing phase diagrams that distinguish ergodic from nonergodic behavior.

Contribution

It introduces a dynamical approach using Loschmidt echo to map the interplay between disorder and interactions in many-body quantum systems.

Findings

Identifies regimes of ergodic and nonergodic behavior based on LE dynamics.

Provides a qualitative phase diagram of polarization behavior.

Demonstrates the effectiveness of LE as a dynamical witness in many-body systems.

Abstract

The interplay between interactions and disorder in closed quantum many-body systems is relevant for thermalization phenomenon. In this article, we address this competition in an infinite temperature spin system, by means of the Loschmidt echo (LE), which is based on a time reversal procedure. This quantity has been formerly employed to connect quantum and classical chaos, and in the present many-body scenario we use it as a dynamical witness. We assess the LE time scales as a function of disorder and interaction strengths. The strategy enables a qualitative phase diagram that shows the regions of ergodic and nonergodic behavior of the polarization under the echo dynamics.