Dynamical scaling of Loschmidt echo in non-Hermitian systems

¹ College of Science, Nanjing University of Aeronautics and Astronautics - Nanjing 211106, China
² Key Laboratory of Aerospace Information Materials and Physics (Nanjing University of Aeronautics and Astronautics), MIIT - Nanjing 211106, China
³ Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University - Beijing 100875, China

^(a) tjc.chen@qq.com
^(b) gysun@nuaa.edu.cn (corresponding author)

Received: 17 September 2021
Accepted: 10 February 2022

Abstract

We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.