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Study On Dynamic Properties Of One-Dimensional Random Quantum XXZ Spin System

Posted on:2010-06-02Degree:MasterType:Thesis
Country:ChinaCandidate:X J YuanFull Text:PDF
GTID:2120360275458424Subject:Condensed matter physics
Abstract/Summary:PDF Full Text Request
In this thesis, the dynamics of the 1-D random transverse Ising model and 1-D random XXZ model is investigated by the method of recurrence relations, and the main results are as follows:1. The effects of bimodal, Gaussian and double-Gaussian disorder on the dynamics of the random transverse Ising model with both nearest-neighbor (NN)and next-nearest-neighbor (NNN) interactions are investigated. The results show that in the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. For the Gaussian disorder the dynamical behavior is complex. When the standard deviationsσ_J, (orσ_B)are small the dynamics undergoes a crossover, whileσ_J, (orσ_B) are large enough the crossover disappears. For the double-Gaussian disorder, the results recover to that of the bimodal disorder whenσ_J (orσ_B) are small and to that of the Gaussian disorder whenσ_J(orσ_B)are large.2. The effects of the NNN interactions on the dynamics of the system are studied under three different disordered states. The results show that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as K_i increase, especially when K_i>J_i/2 (J_i and K_i, are exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak (K_i<J_i/2). The effects of the NNN interactions on the dynamics of the system are mainly dependent on the competition between the spin-spin interactions and the external fields.3. The dynamics of the 1-D pure quantum XXZ model with or without external fields is investigated. For the case of non-fields, it is found that there is a Gaussian-like behavior when L (L is the exchange coupling of z spin component) is small, and there is no spin diffusion when L = 1. If there are external fields, the dynamics of the system exhibits more complex behavior which is determined by the external fields and the uniaxial anisotropy of the system.4. The effects of disordered fields on the random XXZ model are studied. The results show that the dynamical behavior is affected by the spin interactions, the disordered fields and the uniaxial anisotropy of the system. For bimodal disorder, the dynamics undergoes a crossover when L is small, and there is no crossover when L is large. For Gaussian disorder, there is a crossover when L and the standard deviationsσ_B are small, and the crossover disappears when L is large. Whenσ_B are large enough, the dynamics is not affected by the value of L .
Keywords/Search Tags:Spin correlation function, Spectral density, Recurrence relations method, Random quantum Ising model, Random quantum XXZ model
PDF Full Text Request
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