Steady-state topological order

Fuente: arXiv
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Main Authors: Dai, Xu-Dong, Wang, Zijian, Wang, He-Ran, Wang, Zhong
Format: Preprint
Published: 2023
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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