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

Abstract

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

CLC Number:

O411.1

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.

References

[1]Valerie Coffman,Joydip Kundu,Wootters William K., Distributed entanglement,Phys. Rev. 2000,A61:052306.
[2]Charles H.Bennett,David P.DiVincenzo(IBM watson Res.Ctr.),John A.Smolin(UCLA),Wootters William K.(Williams Coll.) , Mixed state entanglement and quantum error correction,Phys.Rev.1996,A54:3824=3851
[3]Asher Peres(santa Barbara,KITP),Wootters William K , Quantum Measurements of Finite Durationn,Phys.Rev.1985,D32:1968.
[4]Wootters W K ,TATISTICAL Distance and Hilbert Space,Phys.Rev.D,1981,23:357=362.
[5]Gu Shi-Jian ,Tian Guan-Shan , Entanglement and quantum phase transition,quant-phys.2005,vl 28:0511243. [6] Cao Min and Zhu shiqun,Thermal entanglement between alternate qubits of A four-qubit Heisenberg XX chain in a magneic field. Phys. Rev. A71,034311(2005).
[7] Rossignoli R and Canosa N,Glogal thermal entanglement in n-qubit systems. Phys. Rev. A72,012335(2005) [8] Wang Xiaoguang and Wang Z.D.,Thermal entanglement in ferrimagnetic chains.Phys. Rev. A73,064302(2006)
[9]Zhu Yan,Zhu Shiqun,and Hao Xiang, entanglement in an aisotropic spin-1 Heisenberg XX chain.Phys. Rev. Vol(16),No.8,2007:1009-1963.
[10] 冯端,金国钧. 凝聚态物理学（上卷） [M] —北京：高等教育出版社 2003. 11~13 Feng Rui,Jin Guojun , Condensed matter physics (Volume) [M] —Beijing：Higher Education Press 2003. 11~13.
[11]Pan Feng , permutation group approach to the one-dimrnsional XXX heisenberg open spin-1/2 chains,International Journal of Modern Physics.2004,C15:247-265.
[12]潘峰，张丹.一维海森堡自旋1/2开链模型能量矩阵的规则分形结构[J]辽宁师范大学学报(自然科学版),2002,25(4):372-375. Pan Feng ,Zhang Dan .The regularization structure of energy matrix of the model of Heisenberg open spin-1/2 chains in one dimension
[13]Pan Feng,, Draayer J P ,A Complementary group technique for a resolution of the outer multiplicity problem of SU(n).1.Litterwood rule an a complementary group of SU(n),J.math.Phys.1998,39:5631-5641.
[14]Gu Shijian,Tian Guanshan,Hai Qinglin , Ground-state entanglement in the XXZ model, Phys. Rev. A 71. 052322(2005).
[15] 韩文娟，海森堡链XY模型在一定位型下能谱[J]贵州大学学报(自然科学版) , 2007,第3期（第24卷）: 244~246. Han Wen –juan ,Energy Spectrum of the XY Model of Heisenberg Spin China in a Certain Situation[J] Guizhou University Journal (Natural Science), Vol(24）, NO.3, 2007: 244~246.
[16] 陈立冰,刘玉华,白宜红,路洪,用三粒子纠缠态和Bell态作量子信道实现非局域的态交换(英文) 2006第4期（第23卷）: 489. Chen Libing,Liu Yuhua,Bai Yihong,Lu hong,Implementing a non-local SWAP operation on two entangled pairs by a three-qubit entangled state and a Bell-state. Vol(23),No.4,2006:489.
[17]席拥军，方建兴，朱士群，钱学旻,利用三对纠缠粒子作为通道实现任意三粒子量子态的概率传送, 2006第1期（第23卷）: 61. Xi Yongjun,Fang Jianxing ,Zhu Shiqun,Qian Xuemin,Probabilistic Teleportation of an arbitrary three-particle entangled state via three pairs partly entangled particles. Vol(23),No.1,2006:61.
[18] 计新,张寿,利用两个 EPR对隐形传送三粒子纠缠态 , 2006第6期（第23卷）:816. Ji Xin,Zhang Shou ,Teleportation of the three-particle entangled state By the two EPR pairs. Vol(23),No.6,2006:816.
[19] Hao Xiang, Zhu Shiqun ,Entanglement in a spin-s antiferromagnetic Heisenberg chain. Phys. Rev. A 72. 042306( 2005)
[20] BENNETT C H et al. Mixed –state entangement and quantum error correction[J]. Phys Rev A, 1996,54:3824-3851.
[21] Ren Jie, Zhu Shiqun , Density-matrix renormalization-group study of entanglement and entropy in an antiferromagnetic Heisenberg spin chain with domain walls.Phys. Rev. A 77. 034303(2008).
[22] VEDRAL V et al, quantum entangement [J]. Phys Rev Lett,1997,78:2275-2279.
[23] Wang Xiao guang ,Boundary and impurity effects on the entanglement of Heisenberg chains. Phys. Rev. E 69. 066118(2004) .
[24] 查新未,三粒子量子态隐形传送的正交完备基展开与算符变换, 2007年第2期（第24卷）: 179. Zha Xinwei,Expansion of orthogonal complete set and transformation operator in teleportation of three-particle entangled state. Vol(24),No.2,2007:179.
[25] 朱爱东,张寿,用三态粒子的直积态进行量子密钥分配及受控量子直接通讯 , 2007,第3期（第24卷）: 316.