Spin-correlation functions and susceptibilities in the easy-planeXXZchain

Abstract

We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane $\mathrm{XXZ}$ 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 wave numbers, temperatures, and anisotropy parameters $\ensuremath{-}1<~\ensuremath{\Delta}<~1.$ In the easy-plane ferromagnetic region $(\ensuremath{\Delta}<0),$ the longitudinal correlators of spins at distance n change sign at a finite temperature ${T}_{0}(n,\ensuremath{\Delta}),$ 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.