Topologically Ordered Steady States in Open Quantum Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914600347238400 |
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| author | Wang, Zijian Dai, Xu-Dong Wang, He-Ran Wang, Zhong |
| author_facet | Wang, Zijian Dai, Xu-Dong Wang, He-Ran Wang, Zhong |
| contents | The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12482 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topologically Ordered Steady States in Open Quantum Systems Wang, Zijian Dai, Xu-Dong Wang, He-Ran Wang, Zhong Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems. |
| title | Topologically Ordered Steady States in Open Quantum Systems |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2306.12482 |