A Quasi One-dimensional Heisenberg Antiferromagnetic Systems Antiferromagnetic

In this thesis, a kind of quasi-one-dimensional (QOD) Antiferromagnetic Heisenberg (AFII) system is studied by using the density matrix renormalization group (DMRG). This QOD model is constructed by periodically doping S = 1/2 spins (side spin) beside every other spin site on one dimension AFH chain. η = J₂/J₁ (J₁ is theexchange integral on the chain, and J₂ the interaction between side spin and itsnearest neighbor spin on the chain). This thesis emphasizes on the effect of side spins on the physics of the spin chain. It consists of four parts:The first part is the introduction on the studying of the quasi-one-dimensional spin system.The second part mainly introduces the well-known Lieb-Mattis theorem and some important physics conceptions such as spin correlation functions, total spin, order parameter and so on.The third part describes the exact diagonalization based on the Lanczos technique and the DMRG method. The DMRG method is extensively used in the studying of the one-dimensional system.The last part includes our numerical results about the QOD model. ① There are two different spin excitations. The excitation to spin S_G -1 is gapless, but that toS_G +1 gapped. (2) The effective interaction between the nearest spins on the chainbecomes more and more weaker with increasing of η (3) With the increasing of η, the effective interaction between side spin and its nearest neighbor spin on the chain increases in the almost linear way, and the probability (ρ) of dimmer nonlinearlyenhances. Even when 77 is not very large, it is close to 1 {rj = 10,/? = 0.99459). (4) At the thermodynamics limit, the average values < Sf > show that the magnetic order on the chain gets stronger at first then weaker with increasing of rj. The magnetic orderbecomes strongest at 77 0.8. Also, the comparison of our numerical results andconclusions by spin wave theory (SWT) shows that the SWT underestimates quantum fluctuation for this kind of spin system.