# Characterizing time-irreversibility in disordered fermionic systems by the effect of local perturbations

## TL;DR

This paper investigates how local perturbations reveal time-irreversibility in disordered fermionic systems, showing different decay behaviors of the Loschmidt echo and memory retention in localized phases.

## Contribution

It introduces a comparative analysis of time-irreversibility across non-interacting and interacting disordered fermionic models using Loschmidt echo and local observable measurements.

## Key findings

- Exponential decay of LE in ergodic phase
- Algebraic decay of LE in localized phase
- Memory loss in many-body localized systems

## Abstract

We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time-irreversibility. We focus on three different systems, the non-interacting Anderson and Aubry-Andr\'e-Harper (AAH-) models, and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave-functions by measuring the Loschmidt echo (LE). We show that in the extended/ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the long-time limit, in contrast to the non-interacting localized phase where some memory is always preserved.