Dynamic transition of the density-matrix topology under parity-time symmetry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909353750036480 |
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| author | Wang, Wenzhi Yi, Wei |
| author_facet | Wang, Wenzhi Yi, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamic transition of the density-matrix topology under parity-time symmetry Wang, Wenzhi Yi, Wei Quantum Physics 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. |
| title | Dynamic transition of the density-matrix topology under parity-time symmetry |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.14776 |