Eigenvectors of Baxter-Bazhanov-Stroganov τ^{(2)}(t_q) model with fixed-spin boundary conditions

Details Eigenvectors of Baxter-Bazhanov-Stroganov τ^{(2)}(t_q) model with fixed-spin boundary conditions Eigenvectors of Baxter-Bazhanov-Stroganov τ^{(2)}(t_q) model with fixed-spin boundary conditions

2007-05-22

arxiv.org/abs/0705.3236v2

Theoretical and Mathematical Physics, 155(1): 585-597 (2008)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, Janu

Scientific paper

10.1007/s11232-008-0048-1

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.

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