Exact solution of a generalized two-sites Bose-Hubbard model

TL;DR

This paper presents an exact solution to a generalized two-sites Bose-Hubbard model with asymmetric tunnelling using an algebraic Bethe ansatz approach, revealing a geometric structure of the Bethe equations in the non-interacting limit.

Contribution

It introduces a new parametrization of the bosonic Lax operator and solves the model exactly, extending the algebraic Bethe ansatz method to asymmetric tunnelling scenarios.

Findings

Bethe ansatz equations form an $S^{N-1}$ sphere in the no interaction limit

Provides an exact analytical solution for the generalized two-sites Bose-Hubbard model

Enhances understanding of integrable models with asymmetric tunnelling

Abstract

I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.