Spin-Peierls Transition in Quantum Antiferromagnets

近年来，由晶格位移引起的自旋Peierls相变引起了人们的广泛关注。本研究的目的是研究晶格畸变对s-P跃迁的影响，重点是动力学方面，具体研究了一维量子反铁磁系统和量子三角海森堡系统。（1）在晶格畸变δ（T）随温度变化的S=1/2一维XY反铁磁体的特殊情况下，允许进行严格的计算，从而阐明了s-P跃迁的内禀动力学行为。(2)本文在Hartree-Fock近似下，用二次绿色函数研究了一维海森堡反铁磁体（作为真实的s-P磁体CuGeO_3的模型）。新的功能的发病被澄清的动态磁化率和良好的协议与rcent中子散射测量的结果被发现在这种材料。(3)最近的实验研究指出，次近邻相互作用J_2对s-P跃迁起着重要的作用，它与近邻相互作用J_1竞争。讨论了竞争效应对系统动力学行为的影响。(4)研究了一维反铁磁系统的非线性磁激励。(5)本文用玻色子平均场理论研究了S=1/2海森堡三角形晶格位移耦合反铁磁系统。(6)研究了磁场对s-P跃迁的影响。

The recent observation of spin-Peierls transition induced by the lattice displacement has attracted considerable attention. The purpose of this research is to investigate the effect of the temperature- dependent lattice distortion on the s-P transition with emphasis on the dynamics.Concretely, 1-D quantum Antiferromagnetic system and quantum triangular Heisenberg system are investigated. Obtained results are following :(1) In the special case of S=1/2 1-D XY antiferromagnet with the temperature dependent lattice distortion delta (T), the rigorous calculations are allowed, so that intrinsic dynamical behavior of s-P transitions are elucidated.(2) For S=1/2 1-D Heisenberg antiferromagnet, which is considered as a model of the real s-P magnet CuGeO_3, is studied by means of two-time Green functions within the Hartree-Fock approzimation. The onset of new features are clarified in the dynamical susceptibility and good agreement with the results of the rcent neutron scattering measurement is found in this material.(3) Recently, it is pointed out experimentally that the next nearest neighbor interaction J_2, which competes with the nearest neighbor one J_1, plays important role to s-P transition. The competing effects on the dynamical behavior are also discussed.(4) Nonlinear magnetic excitation is studied on 1-D antiferromagnetic system.(5) The S=1/2 Heisenberg triangular sntiferromagnetic system coupled with lattice displacements is studied by boson mean-field theory.(6) The magnetic field effects on s-P transtion is also investigation.