Free field construction for the eight-vertex model: representation for form factors

TL;DR

This paper extends the free field realization of the eight-vertex model to include form factors, providing explicit calculations for specific operators, and linking corner transfer matrices of different models.

Contribution

It introduces a novel construction of form factors in the eight-vertex model using free field realization and establishes a relation between corner transfer matrices of two models.

Findings

Explicit two-particle form factor of the σ^z operator calculated.

Extended free field realization to include form factors.

Established relation between corner transfer matrices of eight-vertex and SOS models.

Abstract

The free field realization of the eight-vertex model is extended to form factors. It is achieved by constructing off-diagonal with respect to the ground state sectors matrix elements of the $\Lambda$ operator which establishes a relation between corner transfer matrices of the eight-vertex model and of the SOS model. As an example, the two-particle form factor of the $\sigma^z$ operator is evaluated explicitly.