Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet

TL;DR

This paper develops integral solutions to the quantum Knizhnik-Zamolodchikov equations for the Heisenberg XYZ antiferromagnet's correlation functions, connecting them with cyclic SOS models and exploring their relations to existing formulas.

Contribution

Introduces two integral solutions for the correlation functions of the XYZ model, extending previous models and improving summation techniques.

Findings

First integral solution derived from cyclic SOS model

Second integral solution with higher-fold integrals for parameter r

Relations among new formulas and existing correlation function formulas

Abstract

Presented are two kinds of integral solutions to the quantum Knizhnik-Zamolodchikov equations for the 2n-point correlation functions of the Heisenberg XYZ antiferromagnet. Our first integral solution can be obtained from those for the cyclic SOS model by using the vertex-face correspondence. By the construction, the sum with respect to the local height variables k_0, k_1, >..., k_{2n} of the cyclic SOS model remains other than n-fold integral in the first solution. In order to perform those summations, we improve that to find the second integral solution of (r+1)n-fold integral for r in Z_{>1}, where r is a parameter of the XYZ model. Furthermore, we discuss the relations among our formula, Lashkevich-Pugai's formula and Shiraishi's one.