Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature

TL;DR

This paper derives algebraic formulas for the density matrices of finite segments of the integrable isotropic spin-1 chain at arbitrary temperature, providing explicit results for small segments and zero temperature correlations in elementary form.

Contribution

It introduces explicit algebraic expressions for the density matrices of the spin-1 chain at any temperature, including elementary forms of zero-temperature correlations.

Findings

Explicit formulas for 2 and 3 site density matrices at arbitrary temperature

Elementary form of zero-temperature correlation functions using Riemann zeta functions

Provides a foundation for analyzing finite segment correlations in integrable spin chains

Abstract

We derive algebraic formulas for the density matrices of finite segments of the integrable su(2) isotropic spin-1 chain in the thermodynamic limit. We give explicit results for the 2 and 3 site cases for arbitrary temperature T and zero field. In the zero temperature limit the correlation functions are given in elementary form in terms of Riemann's zeta function at even integer arguments.