Integrable model of bosons in a four-well ring with anisotropic tunneling

TL;DR

This paper presents an exactly solvable four-well bosonic model with anisotropic tunneling, derived via the Quantum Inverse Scattering Method, revealing multiple pseudovacua and a class of eigenstates with simple energy formulas.

Contribution

It introduces a novel integrable four-well bosonic model with anisotropic tunneling, solved through algebraic Bethe Ansatz, expanding the class of exactly solvable many-body systems.

Findings

Multiple pseudovacua are necessary for a complete Bethe eigenstate set.

Existence of eigenstates with simple, closed-form energy expressions.

Model derived from Yang-Baxter equation using Quantum Inverse Scattering Method.

Abstract

We introduce an integrable, four-well ring model for bosons where the tunneling couplings between nearest-neighbour wells are not restricted to be equal. We show how the model may be derived through the Quantum Inverse Scattering Method from a solution of the Yang--Baxter equation, and in turn solved by algebraic Bethe Ansatz means. The model admits multiple pseudovaccum states. Numerical evidence is provided to indicate that all pseudovacua are required to obtain a complete set of Bethe eigenstates. The model has the notable property that there is a class of eigenstates which admit a simple, closed-form energy expression.