Short-distance thermal correlations in the massive XXZ chain

TL;DR

This paper computes short-distance static correlation functions in the massive XXZ chain across various parameters, revealing crossover phenomena and demonstrating the efficiency of factorized formulas for different regimes.

Contribution

It extends previous results to the full parameter plane of the antiferromagnetic XXZ chain, providing efficient numerical methods for correlation functions in various regimes.

Findings

Computed two-point functions for 2, 3, and 4 sites as functions of temperature and magnetic field.

Extended results to the full parameter plane, including the isotropic and Ising limits.

Discovered crossover phenomena induced by quantum fluctuations near critical fields.

Abstract

We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime $\Delta>1$, extending our previous results to the full parameter plane of the antiferromagnetic chain ($\Delta > -1$ and arbitrary field $h$). The factorized formulae are numerically efficient and allow for taking the isotropic limit ($\Delta = 1$) and the Ising limit ($\Delta = \infty$). At the critical field separating the fully polarized phase from the N\'eel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite $\Delta$ inducing unexpected crossover phenomena in the correlations.