An exact solution of the homogenous trimer Bose-Hubbard model

Document Type

Article

Publication Date

3-1-2023

Abstract

It is shown that the homogenous three-site (trimer) Bose-Hubbard model with a periodic boundary condition can be solved exactly by using an extended Bethe ansatz based on the solution of the dimer model and the site-permutation symmetry. A solution of the model within the S 3 symmetric or non-symmetric subspace is presented. Coupled differential equations of a series of extended Heine-Stieltjes polynomials, the zeros of which are related to the solution of the model, are derived. Numerical examples of the solution of the model with N ⩽ 4 bosons, including the related Heine-Stieltjes polynomials and the Van Vleck polynomials, are presented, which serve to validate the procedure and illustrate the completeness of the solutions they render.

Publication Source (Journal or Book title)

Journal of Statistical Mechanics Theory and Experiment

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