Dynamics of one-dimensional random quantum XY system with Dzyaloshinskii–Moriya interaction

In this paper, the effects of random variables on the dynamics of the s=1/2 XY model with the Dzyaloshinskii–Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δ_j (or the standard deviation of random external field δ_B) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δ_J (or δ_B) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.