Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet

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.

26 pages, LaTex2e; A reference is added and a few errors are corrected

References in corpus (4)

• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations
• Free field construction for the eight-vertex model: representation for form factors
• Smirnov-type integral formulae for correlation functions of the bulk/boundary XXZ model in the anti-ferromagnetic regime

Cited by in corpus (3)

• Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
• Form factors, correlation functions and vertex operators in the eight-vertex model at reflectionless points
• Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model