With Sharp Neighbour Ferromagnetic Antiferromagnetic Resistance Spin Quantum Phase Transition Of The Model

In the past few years, a great deal of interest has been concentrated on the frustrated spin system. The frustration usually has two aspects:one from the geometric, and the other from the next-nearest-neighbor interaction in the system. Because of strong quantum fluctuations in the low-dimensional system, the majority of the theoretical model can not be strictly solved. Even though some models can be strictly solved, quantum fluctuations radically modify the classical picture. The quantum phase diagram of system is different from the corresponding classical phase diagram. Therefore a variety of numerical simulation methods have emerged one after another.The most typical numerical methods which can effectively deal with one-dimensional or quasi-one-dimensional quantum spin system are as follows:the exact diagonalization (ED), quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) methods. We will use density matrix renormalization group (DMRG) method which is developed by S. R. White and some others. DMRG method has achieved a great success in calculation of the one-dimensional strongly correlated systems. It overcomes the quantum Monte Carlo method which have negative symbol and the exact diagonalization methods which can only deal with limited number of grid points.This thesis study the next-neighboring antiferromagnetic(AF) frustration effect in the quasi-one dimensional ferromagnetic(FM) Heisenberg model. The section of the thesis includes five chapters:In Chapter I, we introduce the background and significance of quantum spin model. It mainly includes AF Heisenberg model and Haldane conjecture、the n-leg ladder systems, spin-S anisotropic AF Heisenberg spin ladder model, and the FM model which has recently attracted great attention. Half integer-S or inter-S、the competition between the spin-spin exchange interactions and other factors in the system all can affect the properties of the ground state.In chapter Ⅱ, we introduce numerical methods and the order parameters which are mainly used in our thesis. We introduce the exact diagonalization, Lanczos diagonalization, NRG, and DMRG methods, the ALPS software and the order parameters such as ground state energy, spin gap, spin correlation functions.In chapter Ⅲ, we investigate the diagram of the frustrated one-dimensional S=1 anisotropic FM Heisenberg spin model, in which the nearest neighboring interactions are anisotropic FM and the considerable next-nearest-neighboring exchanges are AF. The ground state energy and both the in-plane and out-of-plane spin correlation functions are calculated. Apart from the FM phase and the spin-fluid phase in the small frustration region, we identify E-Ⅰ and E-Ⅱ phase whose spin correlations decay with a short-range exponential law and an oscillating behavior, and S-E phase in the intermediate region. The result is different from the previous result for S=1/2.In chapter Ⅳ, we perform a systematic investigation on a symmetric zigzag spin ladder with inter-leg exchange integrals J1(FM) and inner-leg exchange integrals J2(AF). Under the periodic boundary conditions and in the finite-size system, the ground state energies and their first order derivatives dE/dJ2and the spin-spin correlation are calculated. There appear four plateaus and three steps of abrupt transition in both the function images of dE/dJ2-J2and the spin-spin correlation. It can be concluded that the system have four kinds of quantum states as the frustration strength varies. We give the corresponding spin configurations in the four kinds of quantum states. In the thermodynamic limit, there is just one critical point where the ground state transfers from the FM state to the incommensurate state.In chapter Ⅴ, The shortage and further research are also mentioned.