Quench Dynamics of Entanglement Transition in PT symmetric non-Hermitian system

Previous study shows that the quench dynamics of the long-time steady states under the parity-time (PT) symmetric non-Hermitian Hamiltonian signals the entanglement transition triggered by a level crossing [1]. In this work, we extend previous analysis to physical observables, generic entanglement entropy, and quantum geometry of the PT symmetric non-Hermitian quench dynamics using the biorthonormal basis. These quantities capture not only the level crossings but also the full PT-symmetry transition. In the PT-unbroken phase, these quantities oscillate over time. On the other hand, in the PT-broken phase, these quantities grow exponentially. We demonstrate these properties in both the Yang-Lee model and the non-Hermitian Su-Schrieffer-Hegger (SSH) model.

[1] Shao-Kai Jian, Zhi-Cheng Yang, Zhen Bi, and Xiao Chen Phys. Rev. B 104, L161107 (2021)