Dynamical scaling of Loschmidt echo in non-Hermitian systems

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. Copyright (C) 2022 EPLA

Automated summary

We demonstrate that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of the Loschmidt echo. By numerically studying a non-Hermitian transverse field Ising model, we investigate the quantum criticality through finite-size dynamical scaling of the Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous exact diagonalization results. Furthermore, we introduce a simple method to detect quantum phase transitions using the short-time average of the rate function, motivated by the critically enhanced decay behavior of the Loschmidt echo. Our studies illustrate how to detect equilibrium many-body phase transitions using biorthogonal Loschmidt echo, which can be observed in future experiments through quantum dynamics after a quench.