Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain

TL;DR

This paper derives finite temperature integral formulas for two-point correlations in the antiferromagnetic XXZ chain, providing a rigorous proof of the density matrix integral formula and extending understanding of thermal correlations in quantum spin chains.

Contribution

It introduces finite temperature integral formulas for the XXZ chain's two-point correlations and proves the foundational density matrix integral formula.

Findings

Derived finite temperature correlation formulas

Provided a proof for the density matrix integral formula

Extended the theoretical framework for thermal quantum spin chains

Abstract

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length $m$. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.