Abstract
The periodic Zn-Belavin model on a lattice with an arbitrary number of sites N is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified inhomogeneous T−Q relation. In the special case of N=nl with l being also a positive integer, the resulting T−Q relation recovers the homogeneous one previously obtained via algebraic Bethe Ansatz.
Highlights
Our understanding to phase transitions and critical phenomena has been greatly enhanced by the study on lattice integrable models [1]
Takhtadzhan and Faddeev [12] resolved the model with the algebraic Bethe Ansatz method [7, 13]
We have checked that for a generic w and τ but the number of sites N = nl with l being a positive integer, the inhomogeneous T − Q relations (5.7) can be reduced to homogeneous ones which were previously obtained by the algebraic Bethe ansatz [15, 30]
Summary
Our understanding to phase transitions and critical phenomena has been greatly enhanced by the study on lattice integrable models [1]. By employing the intertwiners vectors [14] which constitute the face-vertex correspondence between the Zn-Belavin model and the associated face model, Hou et al [15] generalized Takhatadzhan and Faddeev’s approach to the Zn-Belavin model with a generic n In their approach, local gauge transformation played a central role to obtain local vacuum states (reference states) with which the algebraic Bethe Ansatz analysis can be performed. Such reference states are so far only available for some very particular number of lattice sites, namely, N = nl with l being a positive integer, but not for the other N This leads to the fact that the conventional Bethe Ansatz methods have been quite hard to apply to the latter case for many years. We adopt ODBA to solve the eigenvalue problem of the periodic Zn-Belavin model with a generic positive integer n ≥ 2 and an arbitrary lattice number N. We discuss the ODBA solution of Zn-Belavin model with twisted boundary condition in Appendix B
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