Abstract The Bose–Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We study the two-site Bose–Hubbard model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices. Besides the inhomogeneous parameters, the model itself has three free boundary parameters, which break the U(1)-symmetry, in other words, break the particle number conservation. The Hamiltonian H under these circumstances is constructed. With the help of the off-diagonal Bethe Ansatz method, we successfully obtain the corresponding Bethe Ansatz equations as well as the eigenvalues.Abstract The Bose–Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We study the two-site Bose–Hubbard model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices. Besides the inhomogeneous parameters, the model itself has three free boundary parameters, which break the U(1)-symmetry, in other words, break the particle number conservation. The Hamiltonian H under these circumstances is constructed. With the help of the off-diagonal Bethe Ansatz method, we successfully obtain the corresponding Bethe Ansatz equations as well as the eigenvalues.

Communications in Theoretical PhysicsDec 1, 20151 citation

An exact solution of the homogenous trimer Bose-Hubbard model

Feng Pan, Aoxue Li, Yingxin Wu +1 more

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.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.

Journal of Statistical Mechanics Theory and ExperimentMar 1, 20232 citations

Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model

J.-B. Bru, T. C. Dorlas

Journal of Statistical PhysicsOct 1, 200326 citations

Exact solution of a generalized two-sites Bose-Hubbard model

Gilberto N. Santos Filho

I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$ -invariant $R$ -matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.

arXiv:1610.07111Oct 23, 20160 citations

Improved Variational Approach to the Two-Site Bose-Hubbard Model

M. Melé-Messeguer, Bruno Juliá-Díaz, A. Polls

arXiv:1108.4851Journal of Low Temperature PhysicsSep 21, 20114 citations

I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the

gl(2)

-invariant

R

-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a

S^{N-1}

sphere, where

N

is the total number of atoms in the condensate.