Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region

TL;DR

This paper simplifies the calculation of next nearest-neighbor correlation functions in the critical spin-1/2 XXZ chain by reducing complex integrals to one-dimensional forms and evaluating them analytically for rational parameters.

Contribution

It introduces a method to reduce multi-dimensional integrals for correlation functions to one-dimensional integrals and provides analytical evaluations for rational parameter values.

Findings

Next nearest-neighbor correlations are expressed as one-dimensional integrals.

Analytical solutions are obtained for certain rational parameter values.

The method simplifies the evaluation of correlation functions in the critical XXZ chain.

Abstract

The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.