Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization

TL;DR

This paper computes the complete eigenstates and eigenvalues of small antiferromagnetic spin-1/2 XXZ chains to analyze their dynamic correlations at various temperatures, revealing concentration of spectral weight and decay behaviors.

Contribution

It provides the first exact diagonalization results for dynamic correlations in the XXZ chain at arbitrary temperature, including detailed spectral and temporal analysis.

Findings

$S^{z}(q, ext{omega})$ is concentrated near the two-spinon continuum boundary.

Intermediate structure factors decay exponentially at high T and large q.

No long-time signatures of spin diffusion observed in time-dependent correlations.

Abstract

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + \Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{\mu}(t) S_l^{\mu} > , (\mu=x,z)$, the dynamic structure factors $S^{\mu}(q,\omega)$, and the intermediate structure factors $I^{\mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,\omega)$ is mainly concentrated on the region $|\omega| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{\mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.