Study On Dynamics Of One-dimensional Random Quntum Spin Systems With Dzaloshinskii-moriya Interaction

The dynamical properties of quantum spin systems have received a great deal of theoreticaland experimental interests in the past decades. Only recently, much attention has been paid to theDzyaloshinskii-Moriya (DM) interaction. In this paper the effects of random variables on thedynamics of the quantum spin systems with DM interaction in high-temperature limit are studiedby means of the recurrence relations method, and the mine results are following:We calculate the time-dependent transverse autocorrelation functions as well as thecorresponding spectral densities of the Ising model with DM interaction for the cases that theexchange couplings between spins, external fields and DM interaction satisfy the threedistributions: the bimodal distribution, Gaussian distribution and double-Gaussian distribution.The results show that the dynamics of the system is mainly depended on the competitionbetween spin-spin interaction and the external field, and it is nothing to do with randomdistribution.When the nearest-neighbor exchange couplingsJ i(or the external transverse fieldsBi)satisfy the bimodal distribution, respectively, the dynamical behavior of one-dimensional randomquantum XY system with DM interaction undergoes a crossover from a central peak behavior toa collective mode one. For the Gaussian distribution, it is found that when the value of standarddeviation of random exchange couplingσ J(or standard deviation of random external magneticfieldσ B) is small, the dynamics of the system undergoes a crossover between a collective-modebehavior and a central-peak one. However, whenσ J (orσ B) is large, the crossover vanishes, andthe system shows a central-peak behavior or the most disordered one.For the double-Gaussian disorder, we find that while it is the same as that of Gaussiandisorder whenσ Jorσ Bis larger, whenσ Jorσ Bis small, the dynamical behavior of the systemis similar to that of the bimodal disorder, as well as this phenomenon is accord withdouble-Gaussian distribution characteristics. It is found that for all the cases considered, thedynamics of the above system is similar to that of the one dimensional random XY model.