With Frustrated Mixed-spin Ladder Model Of Quantum Phase Transitions

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.However, in these spin-Heisenberg models,spin-ladder model which has a special structure between one-dimensional and two-dimensional systems and fascinating Physical properties is a peculiar model in Low-dimensional strongly correlated field.Because of the strong quantum fluctuations in the low-dimensional system, the majority of the theoretical model can not be strictly solved. Therefore a variety of numerical simulation methods have emerged one after another, the most typical numerical methods are: the strict diagonalization (ED), quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) methods.In this thesis, we will use density matrix renormalization group(DMRG) methods which developed by S. R. White and some others, moreover this method has achieved a great success in calculation one-dimensional strongly correlated systems since it was established on. It overcomes the quantum Monte Carlo method which have negative symbol and the strict diagonalization methods which can only handle limited number of grid points.This thesis include two parts, the first half part includes three chapters: In ChapterⅠ, we introduced the purpose and significance. In chapterⅡ, we simply introduced the background of quantum spin models and the main physical background; In chapterⅢ, the DMRG method which is used in our thesis is described.In the second part, the numerical results are presented. This part has two chapters. In the chapterⅣ, a mixed-ladder with frustration is studied. As the change of the frustration parameterα( J x/ J), this model in its classical case exhibits three different phases such as the ferrimagnetic phase ( 0≤α<0.322), the canted phase ( 0.322 <α< 0.461), and the collinear phase ( 0 .461≤α<1). In quantum case, our calculations by the DMRG show that the system exhibits the ferrimagnetic phase when 0≤α< 0.341, the canted phase when 0.341 <α< 0.399 and the disordered phase when 0.399 <α≤1.Obviously, as a result of quantum fluctuations, the quantum canted phase occurs only in a narrow parameter region. Moreover, we found out the system has the similar nature to the model of S=3/2 Heisenberg antiferromagnetic chain whenα=1.In the fifth chapter, a quasi-one-dimensional Heisenberg antiferromagnetic chain with the breaking of sublattice symmetry is investigated. It is shown that the adding of side spins can weaken the correlations between near-neighbor spins while strengthen those between long-range spins. Because of the broken of sublattice symmetry by side spins, the ferromagnetic and the antiferromagnetic long range orders can coexist in the ground state. Side spins can lower the quantum fluctuations, and the effect will weaken as the increasing of interaction distance. The quantum fluctuation of side spin is weakest. But for the 1/5-doped antiferromagntic chain, the quantum fluctuation leads to the 47% loss of its staggered susceptibility. The magnetic frustrations from next-nearest-neighbor bonds will drive this system from the magnetic ordered phase into the disordered magnetic phase. And this phase is a quantum disordered phase which has the gap. The numerical calculations show that the critical point is at 0.477.