The Study Of Dynamic Properties Of One-dimensional Quantum Spin Systems

In this thesis, the dynamics of the one-dimensional s =1/2 random transverse Ising system where the exchange couplings and the transverse fields are considered as random variables is investigated by the recursion method, and the main results are as follows:1. Supposing that the exchange couplings (or the transverse fields) satisfy the Gaussian distribution, the effects of this distribution on the dynamics of the system is investigated. Spin autocorrelation functions and corresponding spectral densities of the system are obtained by the numerical calculation. The results show that when the standard deviations δ_j of the exchange couplings (or the standard deviations δ_b of the transverse fields) are small, the dynamics of the system undergoes two crossovers in sequence as the mean value of the exchange coupling (or the transverse field) varies: from a central-peak behavior to a collective-mode one, and then to the Larmor precession of free spins in an external transverse magnetic field. However, when δ_j (or δ_B) is large enough, there is no crossover, i.e., the dynamics of the system shows a central-peak behavior (or a disordered behavior).2. The dynamics of the system is studied when the exchange couplings (or the transverse fields) satisfy the double-Gaussian distribution. The calculated results show that when the standard deviations of the exchange couplings (or the transverse fields) are small, the dynamics of the system undergoes a crossover from a central-peak behavior onto a collective-mode one as the mean value of the exchange coupling (or the transverse field) varies. When the standard deviations of the exchange couplings (or the transverse fields) are large enough, only a central-peak behavior (or a disordered behavior) is found.3. The dynamics of the metastable random ferromagnetic chain with a coverof the antiferromagnetic film is discussed. It is found that the external magnetic field and the quenched random magnetic fields play a more important role in the dynamics of the system than that of the enhanced exchange couplings. Both the external magnetic field and the quenched random magnetic fields drive the spins to do Larmor precession.4. The effects of the diluted bonds and other types of the random bonds on the dynamics of the transverse Ising model are also investigated. The results indicate that for the all types of probability distributions considered, the dynamics of the system always exhibits a central-peak behavior when the standard deviations of the random bonds are large enough.