Quantum Phase Transition Caused By Frustration In Quasi - One - Dimensional Spin System

Frustrated quantum magnetism in low dimensions has received considerable attention in recent decades. It has been found that frustration may induce unconventional quantum magnetism behavior and novel ground state phase diagram, In this thesis, the density matrix renormalization group (DMRG) method was used to investigate the frustration effect in quasi-one-dimensional s=1/2spin model. The ground state phase diagram was obtained through analyzing the ground state energy, excitation energy gap, spin-spin correlations, and entropy. The thesis includes two parts.In the first part there are three chapters. In chapter1, we introduced the purpose and significance of this research. The background for quasi-one-dimensional quantum spin system was given in Chapter2. In chapter3, the DMRG method and the primary physical conceptions used in this thesis are describedIn the second half of this thesis, the main numerical results were presented. In chapter4, the one-dimensional spin chain with the nearest-neighbor (NN) ferromagnetic (FM)-antiferromagnetic (AF) alternative couplings as well as the next-nearest-neighboring FM frustration was studied. The ground state phase diagram in the J2-J3parameter set was produced, which includes three kinds of phases:FM, AF and Dimer. When the frustration is weak, the ground state is in the Dimer phase, which inclueds triplet-dimer and singlet-dimer. When the AF coupling is relatively small but frustration is strong, the ground state changes into the FM state. However, when both AF coupling and frustration are strong enough, the ground state is in the AF state.In chapter5, we performed a systematic investigation on the ground state of an asymmetric spin ladder with NN FM interaction and diagonal AF frustration. When the ladder is strongly asymmetric, there is a finite intermediate frustration region occupied by the canted state phase between FM and AF phases. The phase boundaries are dependent on the asymmetric strength αa. On the other hand, if the asymmetric strength is not strong enough, the ground state just demonstrates a first order phase transition from ferromagnetism to antiferromagnetism with frustration increasing. The phase diagram of frustration versus the asymmetric strength is given.