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

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.

22 pages, no figures

References in corpus (5)

• Double species condensate with tunable interspecies interactions
• Read-Green resonances in a topological superconductor coupled to a bath
• Dynamics of a two-species Bose-Einstein condensate in a double well
• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
• Bethe states for the two-site Bose-Hubbard model: a binomial approach

Cited by in corpus (10)

• Inner products in integrable Richardson-Gaudin models
• Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
• Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Ground-state energies of the open and closed $p+ip$-pairing models from the Bethe Ansatz
• Ground-state energy of a Richardson-Gaudin integrable BCS model
• Read-Green points and level crossings in XXZ central spin models and $p_x+i{p}_y$ topological superconductors
• The Yang-Baxter paradox
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models