The Baxter–Bazhanov–Stroganov model: separation of variables and the Baxter equation

Abstract

The Baxter-Bazhanov-Stroganov model (also known as the τ (2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z N -Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B n (λ) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer matrices of the τ (2) model guarantee non-trivial solutions to the Baxter equations. For the N = 2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.

The τ2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin’s SOV method

“…There, it stands for the functional relations which result from the truncated fusions of transfer matrix eigenvalues. In the case of the τ 2 -model this type of fusion leads to the same type of equation, as it has been derived in [12,13,17,41].…”

Bethe ansatz solutions of the τ 2-model with arbitrary boundary fields

“…It is believed [1,3,50] that the relations (5.1)-(5.5), the analytic property (5.6) and the truncation identity (5.8) allow us to completely determine the eigenvalues Λ(u) of the fundamental transfer matrix t(u) given by (2.17).…”

Off-diagonal Bethe Ansatz solution of the τ 2-model

“…It is believed [1,21,22] that the quasi-periodicity (4.2), the asymptotic behavior (4.3), the analytic property (4.4) and the truncation identity (4.6) completely determine the eigenvalues {Λ k (u)|k = 1, 2, · · · , p} of the fundamental transfer matrix t(u) given by (2.12).…”