Free Field Representation of Quantum Affine Algebra $U_q\widehat{sl_2}$ and Form Factors in Higher Spin XXZ Model

TL;DR

This paper develops a free field realization of quantum affine algebra for the higher spin XXZ model, deriving integral and residue formulas for form factors that connect lattice models with quantum field theory.

Contribution

It introduces a free field realization of type II q-vertex operators and derives integral and residue formulas for form factors in higher spin XXZ models.

Findings

Derived integral formulas for form factors.

Established a residue formula analogous to Smirnov's formula.

Linked lattice model form factors to quantum field theory structures.

Abstract

We consider the spin $k/2$ XXZ model in the antiferomagnetic regime using the free field realization of the quantum affine algebra $\uqa$ of level $k$. We give a free field realization of the type II $q$-vertex operator, which describes creation and annihilation of physical particles in the model. By taking a trace of the type I and the type II $q$-vertex operators over the irreducible highest weight representation of $\uqa$, we also derive an integral formula for form factors in this model. Investigating the structure of poles, we obtain a residue formula for form factors, which is a lattice analog of the higher spin extension of the Smirnov's formula in the massive integrable quantum field theory. This result as well as the quantum deformation of the Knizhnik-Zamolodchikov equation for form factors shows a deep connection in the mathematical structure of the integrable lattice models and the massive integrable quantum field theory.