Dynamical scaling of Loschmidt echo in non-Hermitian systems

TL;DR

This paper investigates how non-Hermitian many-body phase transitions can be identified through the decay of Loschmidt echo, providing a new method for detecting quantum criticality in such systems.

Contribution

It introduces a simple approach to detect quantum phase transitions using short-time averages of the rate function based on Loschmidt echo decay in non-Hermitian systems.

Findings

Critical exponents match previous results from exact diagonalization.

Short-time average of rate function effectively detects phase transitions.

Method applicable to experimental quantum dynamics after a quench.

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.