Spin-Peierls Transition in Quantum Antiferromagnets

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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.