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arXiv · 2306.12482

Topologically Ordered Steady States in Open Quantum Systems

Zijian Wang·Xu-Dong Dai·He-Ran Wang·Zhong Wang
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Abstract

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.

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Zijian Wang, Xu-Dong Dai, He-Ran Wang, Zhong Wang. 2023-06-21. Topologically Ordered Steady States in Open Quantum Systems. https://doi.org/10.21468/scipostphys.17.6.167

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