Spin-Peierls Transition in Quantum Antiferromagnets

最近观察到的由晶格位移引起的自旋-Peierls相变引起了人们的极大关注。本研究的目的是研究随温度变化的晶格畸变对S-P相变的影响，重点研究动力学性质。具体地，研究了一维量子反铁磁系统和量子三角海森伯系统。得到的结果如下：(1)对于具有随温度变化的晶格畸变量(T)的S=1/2一维XY反铁磁体，我们进行了严格的计算，从而阐明了S-P相变的本征动力学行为。(2)在Hartree-Fock近似下，用二次格林函数方法研究了S=1/2一维Heisenberg反铁磁体CuGeO_3。在动力学极化率中阐明了新特征的出现，并与新近的中子散射测量结果很好地吻合。(3)最近实验指出，与最近邻J_1竞争的次近邻相互作用J_2在S-P相变中起着重要的作用。(4)研究了一维反铁磁系统的非线性磁激发。(5)用玻色子平均场理论研究了具有晶格位移的S=1/2海森伯三角反铁磁系统。(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.