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

• URL: http://arxiv.org/abs/2404.14776v2
• Date: Fri, 18 Oct 2024 06:48:55 GMT
• Title: Dynamic transition of the density-matrix topology under parity-time symmetry
• Authors: Wenzhi Wang, Wei Yi,
• Abstract summary: Density-matrix topology can undergo transitions in the corresponding open-system dynamics. We show that a hidden parity-time symmetry can further facilitate it. Remarkably, we find that the dynamic transition can also happen periodically in the parity-time symmetry broken regime.
• Score: 1.5596062401801003
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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