Study On Dynamics Of One-Dimensional Random Quantum Blume-Capel Model

The study of dynamics of random quantum spin chains is of general interest and timely. In this thesis, the effects of disorder on the dynamics of the one-dimensional quantum XXZ system and Blume-Capcl system at the high-temperature limit are investigated, and the main results are as follows:The dynamical properties of the one-dimensional spin-1/2 random quantum XXZ model with external fields are investigated by using the recurrence relations method. The spin autocorrelation functions as well as the spectral densities of the system are calculated in the presence of the exchange couplings that satisfy two types of distributions and the anisotropy parameter takes some special values. For the case of bimodal distribution, the dynamics of the system undergoes a crossover between a collective-mode behavior and a central-peak one with the increasing of the exchange coupling. It is also found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as the anisotropy parameter increases. In the cases of Gaussian distribution, when the standard deviation of the exchange couplings is small, the system shows a crossover, and the central-peak behavior becomes obvious with the anisotropy parameter increasing; while the standard deviation is large enough, the system only shows a central-peak behavior.The effects of disordered on the dynamics of Blume-Capel model are studied when the nearest-neighbor exchange couplings (or the external fields) satisfy three types of distributions by using the same method. The results show that the dynamics of the system is mainly dependent on the competition between spin-spin interaction and the external field, the single-ion anisotropy enhances the central-peak behavior. For the bimodal distribution, the dynamics of the system behaves a crossover between a collective mode behavior and a central peak one when the single-ion anisotropy takes 0; as the single-ion anisotropy increases, the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker. For the Gaussian distribution and double-Gaussian distribution, when the standard deviation is small, the dynamical behavior of the system is similar to that of the bimodal distribution; while the standard deviation is large enough, the system only shows a behavior. We also find that the dynamics of the system has nothing to do with the types of distribution, which is similar to that of the spin-1/2 system.