# Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator

## TL;DR

This paper demonstrates that out-of-time-ordered correlators (OTOCs) can effectively probe excited-state quantum phase transitions (ESQPTs) in quantum many-body systems, providing a new dynamical signature and potential experimental tool.

## Contribution

It introduces the use of OTOC as a probe for ESQPTs in the Lipkin model, revealing distinct dynamical behaviors and establishing the steady-state OTOC value as an order parameter.

## Key findings

- OTOC exhibits distinct evolution in different ESQPT phases
- Steady-state OTOC value signals the presence of ESQPT
- OTC can be used for experimental detection of ESQPTs

## Abstract

As a measure of information scrambling and quantum chaos, out-of-time-ordered correlator (OTOC) plays more and more important role in many different fields of physics. In this work, we verify that the OTOC can also be used as a prober of the excited-state quantum phase transition (ESQPT) in a quantum many body system. By using the exact diagonalization method, we examine the dynamical properties of OTOC in the Lipkin model, which undergoes an ESQPT. We demonstrate that the OTOC exhibits a remarkable distinct evolution behaviors in different phases of ESQPT. Therefore, the presence of an ESQPT in the quantum many body system can be clearly signaled by the different dynamical behaviors of the OTOC. In particular, we show that the steady state value of the OTOC serves as the order parameter of the ESQPT. Our results highlight the connections between the OTOC and ESQPT, which enable one to use OTOC for experimental tests ESQPTs in quantum many body systems.