Bethe ansatz solution to integrable bosonic cube networks

TL;DR

This paper applies Bethe ansatz techniques to solve two integrable bosonic cube network models, deriving equations for their states and energies after a canonical transformation.

Contribution

It introduces a novel application of Bethe ansatz to bosonic networks on a cube graph, including explicit solution formulas and transformations.

Findings

Bethe ansatz solutions are obtained for both Hamiltonians.

Canonical transformations enable the application of Bethe ansatz.

Explicit equations for states and energies are derived.

Abstract

We study two extended Bose-Hubbard-type Hamiltonians representing bosonic networks restricted to the graph of a cube. For both Hamiltonians, we demonstrate that Bethe ansatz methods of solution can be employed after applying a canonical transformation of operators. We provide the resulting Bethe ansatz equations, and corresponding formulae for states and energies of both Hamiltonians.