Smirnov-type integral formulae for correlation functions of the bulk/boundary XXZ model in the anti-ferromagnetic regime

TL;DR

This paper derives integral formulae for correlation functions of the bulk and boundary XXZ models in the anti-ferromagnetic regime, connecting quantum KZ equations with Smirnov-type solutions and bosonization techniques.

Contribution

It provides explicit integral solutions to quantum KZ equations for XXZ models, linking Smirnov-type equations with bosonization methods in the anti-ferromagnetic regime.

Findings

Integral solutions reproduce known bosonization formulae

Connection established between Smirnov-type equations and quantum affine algebra

Applicable to both bulk and boundary XXZ models in anti-ferromagnetic regime

Abstract

Presented are the integral solutions to the quantum Knizhnik-Zamolodchikov equations for the correlation functions of both the bulk and boundary XXZ models in the anti-ferromagnetic regime. The difference equations can be derived from Smirnov-type master equations for correlation functions on the basis of the CTM bootstrap. Our integral solutions with an appropriate choice of the integral kernel reproduce the formulae previously obtained by using the bosonization of the vertex operators of the quantum affine algebra $U_q (\hat{\mathfrak{sl}_2})$.