一维海森堡链格点中不同电子自旋交换构成能量矩阵的方法  

Method of constructing energy matrix by exchange of electron spin in one dimension Heisenberg chain

作　　者：韩文娟[1] 周勋[2] 张太荣[1] 

机构地区：[1]六盘水师范高等专科学校物理系,贵州水城553004 [2]贵州师范大学物理与电子科学学院,贵州贵阳550001

出　　处：《量子电子学报》2009年第3期306-312,共7页Chinese Journal of Quantum Electronics

基　　金：贵州六盘水师范高等专科学校科研项目基金(200806);贵州省教育厅自然科学基金(黔教科2005205);贵州省科学技术基金资助(黔科通J合[2006]2004)

摘　　要：对一维海森堡链格点中不同电子自旋交换如何构成及所构成的能量矩阵进行讨论,为纠缠度和量子计算提供重要依据。研究方法是:一维海森堡链格点被电子填充分为单、双占据及二者共存二种情况。相邻格点中电子自旋交换分两类,第Ⅰ类:相邻格点最相邻电子自旋交换;第Ⅱ类:"间隔"交换,分为"左间隔"与"右间隔"两种交换(即格点左(右)侧电子与相邻格点左(右)侧电子自旋之间的交换)。将一维海森堡体系的哈密顿算符作用于完备基矢(用置换群所构建)形成能量矩阵。计算结果:(1)位型[4,2]的第Ⅰ类自旋交换在格点单、双占据及格点单、双占据共存三种情况时所得矩阵只在对称填充时相同,别况均不同。(2)位型[4,2]在格点双占据的第Ⅱ类与第Ⅰ类自旋交换所形成的矩阵只在格点被对称填充时相同,别况均不同;自旋"左间隔"交换与"右间隔"交换时,同样哈密顿算符作用于同样完备基矢所得矩阵有些相同,有些不同。最后说明所计算的不同位型矩阵的规律及研究意义。The construction energy matrix and characters of the matrixs are introduced when different electron spin exchange in the sites of Heisenberg chain in one dimension. There are three situations that the sites of Heisenberg chain are filled with single electron only, two electrons only, or single and two ＇electrons at the same time. The exchanges of electron spin of the nearest neighbor site are classified into two sorts. The first sort is the exchange of the nearest electron spin. The second sort is the exchange between the left and the left （or the right and the right） electron spin. The Hamiltonian operator of system of Heisenberg chain acts on the complete basis vectors produced with permutation group to form energy matrix. The calculating results are the following. （1）When the sites are filled with single, two electrons and them at the same time, the matrixs of [4,2] are different except for the sites filled with symmetrica election spin. （2）When the sites are filled with two electrons, the matrixs of [4,2] formed in the second sort are different from that in the first sort except for the sites filled with symmetrica election spin. The same Hamiltonian operator acts on the same complete basis vectors to produce same or different matrixs contrast the exchange between the left and the left neighbor electron spin to the exchange between the right and the right neighbor electron spin. Finally, the rules of the matrixs and their studying significance are showed.

关 键 词：量子光学 海森堡链 矩阵 哈密顿算符 电子自旋 基矢 

分 类 号：O411.1[理学—理论物理]