Steady-state topological order
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909010677989376 |
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| author | Dai, Xu-Dong Wang, Zijian Wang, He-Ran Wang, Zhong |
| author_facet | Dai, Xu-Dong Wang, Zijian Wang, He-Ran Wang, Zhong |
| contents | We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize them by complementary approaches based on topological degeneracy of steady states, topological entropy, and dissipative gauge theory. Whereas the (Liouvillian) level splitting between topologically degenerate steady states is exponentially small with respect to the system size, the Liouvillian gap between the steady states and the rest of the spectrum decays algebraically as the system size grows, and closes in the thermodynamic limit. It is shown that steady-state topological order remains definable in the presence of (Liouvillian) gapless modes. The topological phase transition to the trivial phase, where the topological degeneracy is lifted, is accompanied by gapping out the gapless modes. Our work offers a toolbox for investigating open-system topology of steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Steady-state topological order Dai, Xu-Dong Wang, Zijian Wang, He-Ran Wang, Zhong Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize them by complementary approaches based on topological degeneracy of steady states, topological entropy, and dissipative gauge theory. Whereas the (Liouvillian) level splitting between topologically degenerate steady states is exponentially small with respect to the system size, the Liouvillian gap between the steady states and the rest of the spectrum decays algebraically as the system size grows, and closes in the thermodynamic limit. It is shown that steady-state topological order remains definable in the presence of (Liouvillian) gapless modes. The topological phase transition to the trivial phase, where the topological degeneracy is lifted, is accompanied by gapping out the gapless modes. Our work offers a toolbox for investigating open-system topology of steady states. |
| title | Steady-state topological order |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.17612 |