Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra

TL;DR

This paper introduces a class of bosonic models derived from the quasi-Gaudin algebra that are quasi-exactly solvable and lack U(1) symmetry, with exact eigenvalue solutions obtained through algebraic Bethe ansatz.

Contribution

It develops new bosonic models from the quasi-Gaudin algebra that are quasi-exactly solvable and do not conserve particle number, providing exact solutions within this sector.

Findings

Models are quasi-exactly solvable.

Eigenvalues are obtained via algebraic Bethe ansatz.

Models lack U(1) symmetry, indicating non-conservation of particle number.

Abstract

The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious property. These models have the notable feature that they do not preserve U(1) symmetry, which is typically associated to a non-conservation of particle number. An exact solution for the eigenvalues within the quasi-exactly solvable sector is obtained via the algebraic Bethe ansatz formalism.