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Study of Low-dimension Isotropic Heisenberg Spin System

Author: LiAnKang
Tutor: MaLei
School: East China Normal University
Course: Theoretical Physics
Keywords: The low dimension Heisenberg spin system The density matrix renormalization Phase change
CLC: O413.1
Type: Master's thesis
Year: 2009
Downloads: 64
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Abstract


Due to the nature of the low-dimension quantum system has a strong correlation effects corresponding classical physics, Heisenberg ladder spin chain has long been considered to study different quantum phase nature and the ideal system for all types of quantum phase transition in In the past decades, research the many Physics workers dedicated low energy level, as well as the nature of the ground state for the of low dimension Heisenberg spin system. After O (3) nonlinear σ model various theoretical means for Ni (C 2 H 8 N 2 ) 2 NO 2 (of ClO 4 ) and other specific materials experiments can confirm the \low energy level spectroscopy is an integer number, the energy gap, the number of half-integer spin, low energy level spectroscopy will be no gap. Interestingly, the research laboratory for quasi-one-dimensional antiferromagnetic ladder model, similar to the nature of the one-dimensional Heisenberg spin chain based on its the ladder number of the parity. But in addition, the Heisenberg ladder model also has a more complex physical properties, with the exchange interaction change in the parameter space of the ladder to the chain to the coupling, the nature of the system configuration as the ground state with the low-energy excitation of different change. On the other hand some recent studies have shown that the spin ladder model materials in the incorporation of the hole may be transformed into high-temperature superconductors, so it has great practical significance. In this paper, a brief review of the main theory for low dimensional isotropic Heisenberg spin model, select the alternating spin 1/2 antiferromagnetic coupling diagonal ladder model. Does not consider the interaction diagonal, J.Almeida, et al has been given a very clear phase diagram: different | J '/ J |, with the γ is gradually increased, the system will \The transition to the \We want to know added that there will be much change in the nature of the low energy level of the angle ferromagnetic interaction system. In order to more accurately answer this question, we have chosen the numerical density matrix renormalization powerful and effective way of group (DMRG) as a means of research, it is a research nature of the low energy level of low dimensional quantum lattice system. Addition to computing the ground state and the excited state energy in the course of the study, we also calculated the line correlation function with dimer local sequence parameters function to illustrate the nature of the system in which the quantum phase. Finally take given the ladder to the coupling system J c and γ as parameters of the phase diagram. Our results can spin ladder model J.Almeida and Zhu research linking The benefits for low dimensional quantum spin system in the thermodynamic limit, and the nature of the quantum phase transition as well as the understanding of the relevant properties of the materials.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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