Free Field Construction for Correlation Functions of the Eight-Vertex Model

TL;DR

This paper introduces a free field representation for the eight-vertex model's correlation functions, utilizing vertex-face correspondence and Lukyanov's screening operator, reproducing key spectral and polarization results.

Contribution

It presents a novel free field construction for the eight-vertex model's correlation functions using vertex-face correspondence and nonlocal insertions.

Findings

Reproduces the spectrum of the corner transfer matrix.

Derives the Baxter--Kelland formula for average staggered polarization.

Expresses correlation functions in terms of SOS model with nonlocal insertions.

Abstract

A free field representation for the type $I$ vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a nonlocal insertion. This new nonlocal insertion admits of a free field representation in terms of Lukyanov's screening operator. The spectrum of the corner transfer matrix and the Baxter--Kelland formula for the average staggered polarization have been reproduced.