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

J4 ›› 2009, Vol. 26 ›› Issue (3): 306-312.

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

韩文娟¹周勋² 张太荣¹

1 贵州省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

收稿日期:2008-09-05 修回日期:2008-12-29 出版日期:2009-05-28 发布日期:2009-05-07
通讯作者: 韩文娟（1975-），女，河北，硕士生，从事量子多体理论的研究. E-mail:hanwenjuanying@163.com
基金资助:
贵州六盘水师范高等专科学校科研项目基金资助(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)

Method of exchange of electron spin of Heisenberg open spin-1/2 chain in one dimension to produce energy matrix

HAN Wen-Juan, ZHOU Xun, ZHANG Ta-Rong

1 Dept of physics Guizhou Liupanshui Teachers College ,Shui cheng 553004; 2 School of physics electron and sciences Guizhou Normal University,Gui yang 55000

Received:2008-09-05 Revised:2008-12-29 Published:2009-05-28 Online:2009-05-07

摘要/Abstract

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、双占据及二者共存三种情况.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）側电子与相邻格点左（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（用置换群所构建的）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．

关键词: 海森堡链, 矩阵, 哈密顿算符, 电子自旋, 基矢, 占据

Abstract:

The construction 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 ,or with two electrons only,or with 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 heisenterg chain function the complete basis vectors produced with permutation group to form energy matrix. The calculating results are：(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 in the first sort except for the sites filled with symmetrica election spin.The same hamiltonian operator function 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.

Key words: Heisenberg chain, matrix, Hamiltonian operator, electron spin, basis vector, take up

中图分类号:

O411.1

韩文娟周勋张太荣. 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[J]. J4, 2009, 26(3): 306-312.

HAN Wen-Juan, ZHOU Xun, ZHANG Ta-Rong. Method of exchange of electron spin of Heisenberg open spin-1/2 chain in one dimension to produce energy matrix[J]. J4, 2009, 26(3): 306-312.

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