# Probing the excited-state quantum phase transition through statistics of Loschmidt echo and quantum work

## TL;DR

This paper investigates how excited-state quantum phase transitions (ESQPTs) influence nonequilibrium dynamics by analyzing the statistics of Loschmidt echo and quantum work, revealing critical behaviors and localization effects.

## Contribution

It introduces a method to detect ESQPTs through LE and work distributions and determines the critical exponent via finite-size scaling analysis.

## Key findings

- LE and work distributions vary with control parameters.
- A cusplike shape appears in averaged LE and work at the ESQPT critical point.
- Eigenstates become highly localized at the ESQPT critical point.

## Abstract

By analyzing the probability distributions of the Loschmidt echo (LE) and quantum work, we examine the nonequilibrium effects of a quantum many-body system, which exhibits an excited-state quantum phase transition (ESQPT). We find that depending on the value of the controlling parameter the distribution of the LE displays different patterns. At the critical point of the ESQPT, both the averaged LE and the averaged work show a cusplike shape. Furthermore, by employing the finite-size scaling analysis of the averaged work, we obtain the critical exponent of the ESQPT. Finally, we show that at the critical point of ESQPT the eigenstate is a highly localized state, further highlighting the influence of the ESQPT on the properties of the many-body system.