一种准一维反铁磁海森堡自旋系统的DMRG研究

【作者】 陈东芳；

【导师】 刘拥军；

【作者基本信息】 扬州大学 ， 凝聚态物理， 2005， 硕士

【摘要】 本文利用密度矩阵重整化群（DMRG）方法研究了一种准一维反铁磁海森堡自旋系统,即在一维S=1/2反铁磁海森堡链的旁边每隔一个格点周期性地掺杂一个S=1/2自旋（称为侧自旋）,其中侧自旋与链上最近邻格点间的交换积分为J₂,链上最近邻格点间的交换积分为J₁（J₂,J₂>0）,为了方便,取η=J₂/J₁。本文的研究目的是通过数值模拟,利用系统的基态能、能隙、自旋Z分量、自旋关联函数等物理量较细致地讨论了周期性掺杂对一维反铁磁海森堡自旋链基态性质的影响。本文主要分为四个部分: 第一章,对准一维量子自旋系统目前的研究背景和现状作了一个简要介绍,并介绍了本文的研究内容和所采用的研究方法。 第二章,介绍了几个重要的物理概念和著名的Lieb-Mattis定理。其中物理概念主要包括自旋关联函数（长度）、总自旋、序参量等。 第三章,重点介绍了目前常用来研究量子自旋系统的基于Lancz（o|¨）s技术的严格对角化方法和密度矩阵重整化群（DMRG）方法。对密度矩阵重整化群方法中的“无限系统算法”和“有限系统算法”分别作了较详细的介绍。 第四章,介绍了一种准一维反铁磁海森堡自旋模型的数值模拟结果。根据数值计算研究得到:①该准一维系统自旋激发呈现新的特征,S_G→S_G+1激发呈现自旋能隙,S_G→S_G—1没有自旋能隙。②随着参数η的增加,链上最近邻格点自旋间的有效相互作用越来越弱;③随着参数η的增加,侧自旋与链上最近邻格点自旋间的有效作用近似按线性增加,它们形成单态的几率呈非线性增加,即便是η并不是很大,形成dimer的几率也接近于1（η=10,ρ=0.99459）;④在热力学极限下,不同子格的自旋Z分量的计算结果显示,链上格点的磁性序先增强后变弱,在η～0.8处磁性序最强。最后,通过比较DMRG的数值结果利已有的自旋波理沦的更多还原

【Abstract】 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.更多还原