Dynamics of the anisotropic two-dimensional XY model

Abstract

In this paper we study the dynamics of the two-dimensional XY model with single-ion anisotropy, and spin S = 1, in the large D phase, and low temperatures, using the bond operator formalism. The in-plane structure factor is a delta function. The out of plane shows a three peak structure, which merges in a single peak at the Brillouin zone boundary. We analyze also spin currents generated by a magnetic field gradient. The spin conductivity is calculated, at finite temperature, using the Kubo formula. The model shows unconventional ballistic spin transport at finite temperature. The computed spin conductivity exhibits a nonzero Drude weight at finite temperature. For ω 2m, which persist in the zero temperature limit. The conductivity at the critical point, and for small frequencies, is (gμB)2/ħ times a universal scaling function of ħω/kB T.