Level two irreducible representations of $U_q(\widehat{sl}_2)$, vertex operators, and their correlations

TL;DR

This paper constructs explicit vertex operators for level two $U_q(\\widehat{sl}_2)$ modules using bosons and fermions, deriving integral formulas for their traces and applying these to compute spin correlation functions in an integrable quantum spin chain.

Contribution

It provides the first explicit construction of level two vertex operators for $U_q(\widehat{sl}_2)$ and extends correlation function calculations to the $S=1$ case.

Findings

Explicit vertex operators for level two modules are constructed.

Integral formulas for traces of vertex operator products are derived.

$n$-point spin correlation functions for $S=1$ quantum spin chain are obtained.

Abstract

Vertex operators associated with level two $U_q(\widehat{sl}_2)$ modules are constructed explicitly using bosons and fermions. An integral formula is derived for the trace of products of vertex operators. These results are applied to give $n$-point spin correlation functions of an integrable $S=1$ quantum spin chain, extending an earlier work of Jimbo {\em et al} for the case $S=1/2$.