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

TL;DR

This paper derives explicit formulas for the eigenvectors of the Baxter-Bazhanov-Stroganov model with fixed-spin boundary conditions, extending previous periodic case results and solving the associated Baxter equations explicitly.

Contribution

It provides the first explicit eigenvector formulas for the BBS model with fixed-spin boundaries, obtained via a limiting procedure from the periodic case using Sklyanin's separation of variables.

Findings

Explicit eigenvectors for fixed-spin boundary conditions derived.

Solutions to the Baxter equations are obtained explicitly.

Eigenvectors of the Ising-like Z_N quantum chain Hamiltonian are included.

Abstract

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.