Quantum-classical crossover in the spin 1/2 XXZ chain

TL;DR

This paper investigates the quantum-classical crossover in the spin 1/2 XXZ chain by calculating correlation functions at finite temperature, revealing a novel sign change in correlations indicative of a transition from quantum to classical regimes.

Contribution

The study provides the first evidence of a temperature-dependent sign change in correlations in the XXZ chain, highlighting a quantum to classical crossover.

Findings

Correlation functions computed for N=16 and 18 spins.

Identification of temperature and separation regimes with positive and negative correlations.

Observation of a sign change in correlations as a signature of quantum-classical crossover.

Abstract

We compute, by means of exact diagonalization of systems of N=16 and 18 spins, the correlation function <\sigma^z_0\sigma^z_n> at nonzero temperature for the XXZ model with anisotropy \Delta. In the gapless ferromagnetic region -1<\Delta<0 for fixed separation the temperature can always be made sufficiently low so that the correlation is always negative for n \neq 0. However we find that for sufficiently large temperatures and fixed separation or for fixed temperature greater than some T0(\DElta) and sufficiently large separations the correlations are always positive. This sign changing effect has not been previously seen and we interpret it as a crossover from quantum to classical behavior.