Solution of the classical Yang--Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunneling model

TL;DR

This paper introduces a novel solution to the classical Yang-Baxter equation with exotic symmetry, enabling the proof of integrability for a generalized multi-species boson tunneling model beyond traditional methods.

Contribution

It identifies a unique non-skew-symmetric solution to the classical Yang-Baxter equation and applies it to establish integrability of a multi-species boson tunneling model.

Findings

Constructed commuting transfer matrices from the new solution.

Proved integrability of the multi-species boson tunneling model.

Developed a Bethe Ansatz solution without a reference state.

Abstract

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang--Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang--Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunneling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.