Biorthogonal quench dynamics of entanglement and quantum geometry in PT-symmetric non-Hermitian systems

TL;DR

This paper investigates the dynamics of entanglement and quantum geometry in PT-symmetric non-Hermitian systems after a quench, revealing exponential growth and linear decay behaviors linked to biorthogonal formalism.

Contribution

It introduces a biorthogonal approach to analyze quench dynamics in PT-symmetric non-Hermitian systems, highlighting unique growth and decay patterns of quantum quantities.

Findings

Exponential growth of observables after quench into PT-broken phase

Linear decay of TTC entropy in non-interacting fermionic systems

Confirmation of results using Yang-Lee and non-Hermitian XXZ models

Abstract

We explore the quench dynamics of PT-symmetric non-Hermitian systems by utilizing the biorthogonal formalism. We analyze quench dynamics of observable quantities, the quantum geometric tensor, and various entanglement quantities, including the entanglement entropy, the SVD entropy, and the Tu-Tzeng-Chang entropy. Our results show that a sudden quench into a PT-broken phase generally leads to exponential growth in these quantities, driven by the biorthogonal density matrix's non-positivity. In contrast to generic interacting systems, we observe a surprising linear decay in the TTC entropy for non-interacting fermionic systems. This finding originates from the approximate spectral symmetry of the biorthogonal reduced density matrix, and we confirm our findings using the Yang-Lee and non-Hermitian XXZ models.