Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model

TL;DR

This paper develops a vertex operator approach for calculating correlation functions in Belavin's rac{Z}{nZ}-symmetric model, utilizing bosonization and vertex-face transformations to derive explicit expressions.

Contribution

It introduces a vertex operator framework for the rac{Z}{nZ}-symmetric model, enabling the calculation of correlation functions via bosonization and vertex-face transformation techniques.

Findings

Derived explicit bosonized expressions for CTM Hamiltonian and tail operators.

Calculated the spontaneous polarization, confirming previous results.

Established a method to obtain correlation functions in the rac{Z}{nZ}-symmetric model.

Abstract

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the $A^{(1)}_{n-1}$ model. Correlation functions of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result by myselves in 1993.