Spin correlation functions and susceptibilities in the easy-plane XXZ chain

TL;DR

This paper develops a Green's-function theoretical approach to analyze magnetic short-range order in the $S=1/2$ easy-plane XXZ chain, calculating susceptibilities and correlations across all parameters and temperatures.

Contribution

It introduces a self-consistent Green's-function method with vertex parameters to compute static susceptibilities and correlations for the XXZ chain at all anisotropies, temperatures, and wavevectors.

Findings

Longitudinal correlators change sign at finite temperature in the ferromagnetic region.

Uniform static susceptibilities show a maximum due to short-range order effects.

Results agree with recent finite-chain diagonalization data.

Abstract

We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane XXZ chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex parameters. The longitudinal and transverse static susceptibilities and two-point correlation functions of arbitrary range are calculated self-consistently for all wavenumbers, temperatures, and anisotropy parameters $ -1\leq \Delta \leq 1$. In the easy-plane ferromagnetic region $(\Delta < 0)$, the longitudinal correlators of spins at distance $n$ change sign at a finite temperature $T_0(n,\Delta)$, in reasonable agreement with recent data obtained by finite-chain diagonalizations. The temperature dependence of the uniform static susceptibilities exhibits a maximum which is explained as an effect of magnetic short-range order which decreases with increasing temperature.