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.

6 pages, 3 figures

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• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Many-body phase transitions in a non-Hermitian Ising chain
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Anomalous dynamical response of non-Hermitian topological phases
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Dynamical phase transition in a strongly hybridized phonon-triplon chain
• Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model
• Dynamical scaling laws in the quantum $q$-state clock chain
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Higher-order exceptional lines in a non-Hermitian JaynesCummings triangle