Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain

TL;DR

This paper derives polynomial representations for third-neighbor and other four-point correlation functions in the ground state of the spin-1/2 XXZ chain, simplifying complex integral expressions into more manageable forms.

Contribution

It introduces a method to reduce multi-dimensional integrals of correlation functions to polynomials involving one-dimensional integrals, advancing analytical techniques for the XXZ chain.

Findings

Polynomial expressions for third-neighbor correlation functions derived.

Reduction of complex integrals to simpler polynomial forms achieved.

Enhanced analytical understanding of spin correlations in the XXZ chain.

Abstract

The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for -1<\Delta \leq 1 and 1<\Delta. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.