Form factors of spin 1 analogue of the eight-vertex model

TL;DR

This paper develops a method to compute form factors of local operators in the spin 1 twenty-one-vertex model using free field representations, providing explicit integral formulas and a concrete two-particle example.

Contribution

It introduces a free field approach to derive form factors in the spin 1 twenty-one-vertex model, extending techniques from SOS models and vertex-face transformations.

Findings

Constructed tail operators using free bosons and fermions.

Derived multiple integral formulas for form factors.

Explicitly calculated the two-particle form factor of the spin operator.

Abstract

The twenty-one-vertex model, the spin $1$ analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the $2\times 2$-fold fusion SOS model and vertex-face transformation. The tail operators, which translate corner transfer matrices of the twenty-one-vertex model into those of the fusion SOS model, are constructed by using free bosons and fermions for both diagonal and off-diagonal matrix elements with respect to the ground state sectors. Form factors of any local operators are therefore obtained in terms of multiple integral formulae, in principle. As the simplest example, the two-particle form factor of the spin operator is calculated explicitly.