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

Abstract

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + ΔS_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $Δ=0 , \cos(0.3π)$, and 1. The dynamic spin pair correlations $< S_{l+n}^μ(t) S_l^μ > , (μ=x,z)$, the dynamic structure factors $S^μ(q,ω)$, and the intermediate structure factors $I^μ(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,ω)$ is mainly concentrated on the region $|ω| < \varepsilon_2(q)$, 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 $I^μ(q,t)$ for $Δ\neq 0$ 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.