Quasi One-dimensional Ferromagnetic Spin Model Of Antiferromagnetic Drag Down Effect

In the one-dimensional or quasi-one-dimensional strongly correlated systems, there are many novel physical phenomenon, so that the similar systems in condensed matter physics, have always being the focus. In the low dimension quantum system, the interaction between the frustration and quantum fluctuation would diversify the physical properties of quantum system. At present the numerical methods dealing with the quantum systems, usually include Exact Diagonalization, Quantum Monte Carlo and Density Matrix Renormalization Group, and in which the DMRG method is the most powerful tool especially about analyzing one-dimensional or quasi-one-dimensional models. In this thesis, we study the two-leg ladder model with the next-nearest-neighbor anti-ferromagnetic coupling as frustration and ferromagnetic next-nearest interactions, on the quantum phase transition caused by the frustration, by using mainly the Lanczos exact diagonalization method and DMRG technique. Not only will the work have theoretic importance, but also will be helpful to study new nanomaterials.My thesis has two main parts, first one has three chapters:in the first chapter we will give a brief introduction about present research background and current situation of one-dimensional and quasi-one-dimensional system; in the second chapter it will be the fundamental theory about ED method and DMRG technique of the software ALPS(Algorithms and Libraries for Physics Simulations), about which we give an general outline; in the third chapter it will be the introduction to some theoretical models and related physical parameters.In the second part, two chapters show the different results of mixed comb model and mixed ladder model. We found that the frustration lead to different phase transition in two models. In chapter four, we study the next-nearest-neighbor anti-ferromagnetic frustration effect to phase diagram in mixed comb model:in the length L mixed comb model, with the frustration varying, the ground state will transform from the FM state to a S≠0ferrimagnetic region, and then to the AF state, but it will be different in the mixed ladder model. In this part, we analyse the phase transition in mixed comb model, by way of Lanczos diagonalization, DMRG technique and classically analytic method, and we get two critical points0.25and0.45473mentioned above in the thermodynamic limit. And we could draw conclusion that there is a little difference between two results of the analytic method and numerical method.In chapter five, mixed ladder model’s phase diagram will be showed, and we will give the results that as the frustration varies, the ground state transforms from the S=L ferromagnetic state to S=0anti-ferromagnetic state directly in the length L ladder model. In addition, with J1=-1fixed, we analyze the phase transition from ferromagnetic state to S=0AF state and that from the Rung-Singlet to Rung-Triplet state, as the result of the competition between the nearest-neighboring interchain coupling J⊥and the next-nearest-neighbor frustration J2. We give the phase diagram in the parameter space of J⊥and J2, and explain the phase diagram analytically.