Numerical Study Of Ferrimagnetic Heisenberg Model With Frustration

Since the evidence of the existence of a short-range resonating-valence-bond phase approach to the high-Tc superconductivity was found in a sufficiently frustrated Heisenberg model, a great deal of interest has been concentrated on the frustrated spin system. In this thesis, using ED (exact-diagonalization) and DMRG (density matrix renormalization group) methods,we study the effect of magnetic frustrations from next-nearest-neighbor bonds in a quasi-one-dimensional (QOD) antiferromagnetic Heisenberg (AFH) chain, which is ferrimagnetism for weak frustrations. This QOD model is constructed by periodically adding S =1/2 spins (side spin) beside every other spin site in a S= 1/ 2 AFH chain.As the change of the frustration parameterα( = J 2 / J1), this model in its classical case exhibits different phases such as the ferrimagnetic phase (F, 0≤α<1/3), the canted phase (C, 1 /3<α<1) and the collinear phase (N,α>1). The calculation of S GT by ED method shows that the system in the quantum case exhibits the F phase ( 0≤α<0.401), the C phase ( 0 .401<α<0.412) and the disordered phase ( 0 .412<α≤1). Obviously, as a result of quantum fluctuations, the quantum C phase occurs only in a very small region. The quantum disordered phase has no counterpart in the classical case. Our calculations show that the quantum fluctuations favor the magnetic long-range order. A stronger frustration is needed to destroy this magnetic order in quantum case than in the classical case.The DMRG data for the ground state energy per unit cell (GSEPU) and the different long-range spin-spin correlations further support the phase diagram suggested by ED method. Using these DMRG data, we also discuss the effect of frustrations from next-nearest-neighbor interactions in our model. We can conclude:①for the magnetic phase ( the quantum F phase + the quantum C phase), frustrations smoothly reduce the correlations between spins on the linear chain and so the magnetic order becomes weak. But moderate frustrations are able to destroy the magnetic order and to stabilize the quantum disordered phase;②for the disordered phase (0 .412<α≤1), the period of its ground state wave function doubles due to the spontaneous symmetry breaking and the spin gap is opened. As the frustrations increasing, the weight of TD (tetramer-dimer) spin-state density increases from about 0.77 to 1.0, so we can say in some sense that the overlap of the ground state and the TD state is large. Meanwhile the differences of energies between this two kinds of states become smaller and smaller. This result means that the TD state which is the ground state of this model atα=1, is dominant for the ground state in the disordered region.