Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise

TL;DR

This paper derives an exact solution for the spectrum of a dissipative quantum system modeled by a tight-binding chain with dephasing noise, using a mapping to the Hubbard model and Bethe ansatz techniques.

Contribution

It establishes an exact correspondence between a dissipative tight-binding model and a Hubbard model with imaginary interaction, enabling exact spectral analysis.

Findings

Exact Bethe ansatz spectrum for the Liouvillian in 1D

Relation between steady states, decay modes, and Hubbard eta-pairing symmetry

Connection between correlation function evolution and Hubbard model states

Abstract

We construct an exact map between a tight-binding model on any bipartite lattice in presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the non-equilibrium steady state and the leading decay modes describing the relaxation at late times are related to the eta-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time-evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.