Short-distance thermal correlations in the XXZ chain

TL;DR

This paper provides explicit, numerically efficient formulas for short-distance thermal correlation functions in the XXZ chain, covering various parameters and enabling precise calculations in the massless regime.

Contribution

It derives explicit formulas for short-distance correlations in the XXZ chain, extending previous mathematical results to practical, high-precision computations.

Findings

Explicit formulas for 2, 3, and 4 site correlations

Correlations computed across temperature and magnetic field ranges

High-precision results for the massless regime

Abstract

Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in the infinite chain. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field for various anisotropies in the massless regime $- 1 < \Delta < 1$. It turns out that the new formulae are numerically efficient and allow us to obtain the correlations functions over the full parameter range with arbitrary precision.