Dynamical scaling of Loschmidt echo in non-Hermitian systems

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.

Dynamical scaling laws in the quantum $q$-state clock chain

“…( 8) for a small quench in the vicinity of the equilibrium critical point h c . This poses a challenge for using the Loschmidt echo to diagnose the equilibrium criticality if a prior knowledge about the precise value of the critical point h c is absent 21,22 . In the following section, we propose to use a short-time average of the rate function 22 ,…”

“…The nature of phase transitions can usually be charaterized by the universality classes and the order parameters from the renormalization group 2,3 and the finite-size scaling theory 4,5 . Using the theoretical tools of quantum information science, quantum phase transitions and critical phenomena in equilibrium can also be probed by the quantum entanglement [6][7][8] , the ground-state fidelity [9][10][11][12][13][14][15][16][17][18][19] and the Loschmidt echo [20][21][22] . In contrast to the quantum entanglement and the ground-state fidelity, which are properties of the ground state, the Loschmidt echo is a nonequilibrium quantity and is much easier to be measured in experiments upon a sudden quench.…”

“…Recently, the dynamical scaling laws of the Loschmidt echo are established to extract equilibrium critical exponents of manybody systems by the finite-size scaling theory for secondorder phase transitions 21 . For instance, the universality class of phase transitions in one-dimensional Hermitian 21 and non-Hermitian transverse field Ising chain 22 were identified by the Loschmidt echoes.…”

General properties of fidelity in non-Hermitian quantum systems with PT symmetry

“…Research on higher-order transitions with the fidelity susceptibility is still an ongoing interesting topic [3][4][5][6][7][8][9][10]. On the other hand, since the discovery of the parity-time (PT)-symmetric quantum mechanics [11][12][13], the interest of studying quantum phase transitions has recently extended to non-Hermitian systems [14][15][16][17][18][19][20][21][22][23][24][25].…”

Quantum metric unveils defect freezing in non-Hermitian systems

“…Quantum quenches and driving have emerged as tools of choice to explore the non-trivial dynamics of quantum systems [44][45][46][47]. The richness of the emergent phenomenology in Hermitian systems naturally behoves the study of quantum quenches in non-Hermitian systems [34,[48][49][50][51][52]. A famous example of non-trivial dynamics concerns topological defects generated when a coupling is quenched across a quantum critical point [53].…”