Study On Dynamic Properties Of One-Dimension Random Quantum XY Spin System

In this thesis,the dynamics of one-dimensional s=1/2 random XY system in which the exchange couplings and the transverse fields random is investigated by the method of recurrence relations,and the main results are as follows:1.Supposing that the transverse fields(or the exchange couplings)satisfy the double-Gaussian distribution,the effects of this distribution on the dynamics of the isotropic XY system is investigated in the high temperature limit.Spin autocorrelation functions and corresponding spectral densities of the system are obtained by the numerical calculation.The results show that when the standard deviations of the transverse fieldo-σ_B(or the standard deviations of the exchange couplingsσ_J)are small,the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one as the p(the probability of the variable takes the larger mean values in the double-Gaussian distribution)increases.However, whenσ_B(orσ_J)is large enough,the dynamics of the system only shows a disordered behavior (or a central-peak behavior).2.The dynamics of the system is studied when the exchange couplings(or the transverse fields)satisfy the two special cases of the double-Gaussian distribution-Bimodal distribution and Gaussian distribution.The results show that when the transverse fields(or the exchange couplings)satisfy the Bimodal distribution,the system undergoes a crossover from the central-peak behavior to a collective-mode behavior as the ratio of the transverse fields to the exchange couplings increases.For the case that the variable satisfy the Gaussian distribution, whenσ_B(orσ_J)is small,the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one as the mean value of the transverse fields(or the exchange couplings)increases,but whenσ_B(orσ_J)is large enough,the system only shows a disordered behavior(or central-peak behavior).3.The dynamics of the disordered anisotropic XY chain is studied in the high-temperature limit when the exchange couplings and the transverse fields satisfy the Bimodal distribution and the Gaussian distribution.We obtain the conclusion based on the results:the dynamics of the anisotropic XY chain is determined by the competition between the transverse fields and the exchange couplings.