Off-diagonal Bethe Ansatz solution of the $\tau_2$-model

Xiaotian Xu; Junpeng Cao; Shuai Cui; Wen-Li Yang; Kangjie Shi; Yupeng Wang

Off-diagonal Bethe Ansatz solution of the $\tau_2$-model

Mathematical Physics 2015-11-04 v2 Statistical Mechanics High Energy Physics - Theory math.MP

Authors: Xiaotian Xu , Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

Abstract

The generic quantum $\tau_2$ -model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in $\tau_j$ -hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T-Q relation with polynomial Q-functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T-Q relation does indeed give the complete spectrum.

Keywords

bethe ansatz painlevé equations and orthogonal polynomials boundary value problems

Cite

@article{arxiv.1507.03367,
  title  = {Off-diagonal Bethe Ansatz solution of the $\tau_2$-model},
  author = {Xiaotian Xu and Junpeng Cao and Shuai Cui and Wen-Li Yang and Kangjie Shi and Yupeng Wang},
  journal= {arXiv preprint arXiv:1507.03367},
  year   = {2015}
}

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22 pages, 2 figures, 4 tables, published version

Off-diagonal Bethe Ansatz solution of the $\tau_2$-model

Abstract

Keywords

Cite

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