Correlation functions of the integrable spin-s chain

TL;DR

This paper derives integral equations for correlation functions in integrable spin-s chains, providing explicit formulas for the two-site density matrix at zero temperature, revealing connections to Riemann zeta functions.

Contribution

It introduces a general method to compute correlation functions for any spin s in integrable chains at finite temperature, including explicit results for spin-3/2.

Findings

Derived non-linear integral equations for correlation functions

Obtained algebraic expressions for two-site density matrices at zero temperature

Connected density matrix elements to Riemann zeta function values

Abstract

We study the correlation functions of su(2) invariant spin-s chains in the thermodynamic limit. We derive non-linear integral equations for an auxiliary correlation function $\omega$ for any spin s and finite temperature T. For the spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain algebraic expressions for the reduced density matrix of two-sites. In the zero temperature limit, the density matrix elements are evaluated analytically and appear to be given in terms of Riemann's zeta function values of even and odd arguments.