Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elements

TL;DR

This paper advances the understanding of the Z_N-Baxter-Bazhanov-Stroganov model by explicitly calculating norms and matrix elements of local operators, including special results for the Ising model when N=2.

Contribution

It provides explicit formulas for norms and matrix elements in the Z_N-Baxter-Bazhanov-Stroganov model using separation of variables, including solutions for the Ising case.

Findings

Explicit norms and matrix elements derived for the model.

Solution of the Baxter equation for N=2 case.

Form-factors computed for the periodic Ising model.

Abstract

We continue our investigation of the Z_N-Baxter-Bazhanov-Stroganov model using the method of separation of variables [nlin/0603028]. In this paper we calculate the norms and matrix elements of a local Z_N-spin operator between eigenvectors of the auxiliary problem. For the norm the multiple sums over the intermediate states are performed explicitly. In the case N=2 we solve the Baxter equation and obtain form-factors of the spin operator of the periodic Ising model on a finite lattice.