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arXiv:2306.13148 · Physical review. B./Physical review. B

Solvable BCS-Hubbard Liouvillians in arbitrary dimensions

X. W. Dai, Fei Song, Zhong Wang

Published Sep 14, 2023• 11 citations
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Abstract

We construct a solvable Lindblad model in arbitrary dimensions, in which the Liouvillian can be mapped to a BCS-Hubbard model featuring an imaginary Hubbard interaction. The Hilbert space of the system can be divided into multiple sectors, each characterized by an on-site invariant configuration. The model exhibits bistable steady states in all spatial dimensions, which is guaranteed by the fermion-number parity. Notably, the Liouvillian gap exhibits a Zeno transition, below which the Liouvillian gap is linear with respect to the dissipation. We also uncover a generic dimension-dependent gap behavior: In one dimension, the gap originates from multiple sectors with spectral crossing; in higher dimensions, a single sector determines the gap.

DOI
10.1103/physrevb.108.115127

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