Survival Probability of the N\'eel State in Clean and Disordered Systems: an Overview

TL;DR

This paper reviews the quench dynamics of one-dimensional spin-1/2 quantum systems, focusing on the survival probability of the N9el state in both clean and disordered cases, highlighting analytical and numerical insights.

Contribution

It provides a comprehensive overview of analytical and numerical results on the survival probability dynamics in spin-1/2 systems with and without disorder.

Findings

Short-time decay can be faster than exponential, including Gaussian behavior.

Long-time dynamics exhibit power-law decay.

Analytical expressions match numerical simulations well.

Abstract

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the N\'eel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.