A Vertex Operator Approach for Form Factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-Symmetric Model and Its Application

TL;DR

This paper develops a vertex operator method for calculating form factors in Belavin's $(bZ/nbZ)$-symmetric model, using bosonization and vertex-face transformation, with explicit results for the eight-vertex model.

Contribution

It introduces a novel vertex operator approach for form factors in the Belavin model based on bosonization and vertex-face transformation techniques.

Findings

Derived explicit expressions for 2m-point form factors in the eight-vertex model.

Connected form factors of $\sigma^z$ and $\sigma^x$ operators to the vertex operator framework.

Demonstrated the applicability of the method for $n=2$ case.

Abstract

A vertex operator approach for form factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is constructed on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. As simple application for $n=2$, we obtain expressions for $2m$-point form factors related to the $\sigma^z$ and $\sigma^x$ operators in the eight-vertex model.