This article is cited in 3 papers

Eigenvectors of the Baxter–Bazhanov–Stroganov $\tau^{(2)}(t_q)$ model with fixed-spin boundary conditions

N. Z. Iorgov, V. N. Shadura, Yu. V. Tykhyy

N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine

Abstract: We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter–Bazhanov–Stroganov {(}BBS{\rm)} model {\rm(}$N$-state spin model{)} with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin's method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding $T$–$Q$ Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like $\mathbb{Z}_N$ quantum chain model.

Keywords: integrable quantum chain, fixed boundary conditions, method of separation of variables.

Received: 31.03.2008

DOI: 10.4213/tmf6195

 English version: Theoretical and Mathematical Physics, 2008, 155:1, 585–597

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