Steady-state topological order
- URL: http://arxiv.org/abs/2310.17612v1
- Date: Thu, 26 Oct 2023 17:35:16 GMT
- Title: Steady-state topological order
- Authors: Xu-Dong Dai, Zijian Wang, He-Ran Wang, Zhong Wang
- Abstract summary: 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.
- Score: 4.990879531940761
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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