Effects of a magnetic field on the dynamics of the one-dimensional Heisenberg model with Dzyaloshinskii-Moriya interactions

Abstract

We use the method of recurrence relations to investigate the dynamics of the one-dimensional spin-$1/2$ Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction in a magnetic field perpendicular to the DM axis. Our results are valid in the high-temperature limit. We determine exactly the first four recurrants, which produce the time-dependent correlation functions. In order to extend our results to longer times, we introduce a new extrapolation procedure for obtaining higher-order recurrants. Our extrapolation mechanism produces good results when compared to the well-known behavior of the relaxation function in the limit of the $\mathit{XY}$ and isotropic Heisenberg models. The relaxation function and the spectral density function are then analyzed for several values of the external field $B$ for the Heisenberg model with DM interactions in one dimension, in the $T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. We find that the external field produces stronger and faster oscillations in relaxation functions and a suppression of the central peak in the spectral density. That is accompanied by the appearance of a peak centered at a finite frequency, due to enhancement of the collective mode of spins precessing about the external field.