Solvable BCS-Hubbard Liouvillians in arbitrary dimensions

TL;DR

This paper introduces a solvable Lindblad model in arbitrary dimensions that maps to a BCS-Hubbard model with an imaginary interaction, revealing dimension-dependent spectral gap behaviors and bistable steady states.

Contribution

It constructs a new solvable Lindblad model in arbitrary dimensions with a mapping to a BCS-Hubbard model, highlighting dimension-dependent spectral properties and phase transitions.

Findings

The model exhibits bistable steady states across all dimensions.

The Liouvillian gap shows a Zeno transition with dissipation.

Dimension-dependent gap behavior: multiple sectors in 1D, single sector in higher dimensions.

Abstract

We present the construction of a solvable Lindblad model in arbitrary dimensions, wherein the Liouvillian can be mapped to a BCS-Hubbard model featuring an imaginary interaction. The Hilbert space of the system can be divided into multiple sectors, each characterized by an onsite 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.