Correlation functions of the integrable $SU(n)$ spin chain

TL;DR

This paper develops a framework for calculating short-range correlation functions in $SU(n)$ integrable spin chains, providing explicit solutions for the $SU(3)$ case at zero temperature, revealing complex non-factorizable correlations involving Hurwitz zeta functions.

Contribution

It introduces a consistent method for computing correlation functions in $SU(n)$ spin chains, including explicit solutions for $SU(3)$ at zero temperature, highlighting differences from the $SU(2)$ case.

Findings

Correlation functions are expressed in terms of Hurwitz zeta functions.

Correlation functions in $SU(3)$ are non-factorizable.

Explicit two- and three-site correlation solutions are provided for $SU(3)$ at zero temperature.

Abstract

We study the correlation functions of $SU(n)$ $n>2$ invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the $SU(3)$ case at zero temperature. The correlators do not seem to be of factorizable form. From the two-sites result we see that the correlation functions are given in terms of Hurwitz' zeta function, which differs from the $SU(2)$ case where the correlations are expressed in terms of Riemann's zeta function of odd arguments.