Dynamic transition of the density-matrix topology under parity-time symmetry

TL;DR

This paper investigates how parity-time symmetry influences the dynamic topological transitions of density matrices in open quantum systems, revealing conditions under which these transitions occur and their periodic nature.

Contribution

It demonstrates that hidden parity-time symmetry can facilitate dynamic topological transitions in density matrices governed by non-Hermitian damping matrices.

Findings

Density-matrix topology transitions occur in the parity-time unbroken regime.

Dynamic transitions can also happen periodically in the parity-time broken regime.

A concrete model illustrates the phase diagram and transition conditions.

Abstract

Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic topological transition, we show that a hidden parity-time symmetry can further facilitate it. Considering the Lindbladian dynamics of a fermionic Gaussian state, we extract the time-evolved density-matrix topology from the single-particle correlation, whose dynamics is governed by a non-Hermitian damping matrix. We show that, for a parity-time symmetric damping matrix and a chiral symmetric correlation matrix, a dynamic transition in the density-matrix topology necessarily occurs in the parity-time unbroken regime where eigenvalues of the damping matrix are real. We illustrate our results using a concrete model, and map out the dynamic phase diagram.Remarkably, we find that the dynamic transition can also happen periodically in the parity-time symmetry broken regime.