Discussion on implementation of a parallel algorithm about Heisenberg mode

Abstract

Abstract: The shortest time of the minimum eigenvalue of. [N，k] of the Heisenberg model( N is the total number of sites of heisenberg chain , k is the number of electrons at site spin up) are obtained using parallel algorithm (Z equisection method ) in fortran program . The studying method is the following . (1)The energy matrix of [N，k] is produced by permutation group. The eigenvalues are obtained diagonalling the energy matrix. The shortest (or longest)time of the minimum eigenvalue of [N，k] is obtained from the data group being made up of the eigenvalues using Z equisection method .The studying results are the following. The time is the shortest. and same when Z is 1 or the number of the eigenvalue of [N, k].(2) When Z and N (k) are same and k（N）increases,the time acquisiting the minimum eigenvalues of [N, k] increases.

Key words: quantum optics, parallel algorithm, eigenvalue, Heisenberg model, time

CLC Number:

O431.2

HUANG Min, HAN Wen-juan, LIU Hai . Discussion on implementation of a parallel algorithm about Heisenberg mode[J]. J4, 2014, 31(1): 80-85.

References

[1]Bose Sougato. Quantum Communication through an Unmodulated Spin Chain[J].Phys. Rev. Lett, 2003，91：207901.
[2]Ji Xin,Zhang Shou .Teleportation of the three-particle entangled state By the two EPR pairs[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2006, 23(6):816-819(in Chinese).
[3]Zha Xinwei . Expansion of orthogonal complete set and transformation operator in teleportation of three-particle entangled state[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2007, 24(2):179-182(in Chinese).
[4]Zhu Aidong , Zhang Shou . Quantum key distribution and controlled quantum direct Communication applying product state of qutrit[J]. Chinese Journal of Quantum Electronics(量子电子学报), 2007, 24(3):316-322(in Chinese).
[5] Chen Libing,Liu Yuhua,Bai Yihong, et al.Implementing a non-local SWAP operation on two entangled pairs by a three-qubit entangled state and a Bell-state[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2006,23(4):489-493(in Chinese).
[6] Gu Shijian,Tian Guanshan,Hai Qinglin.Ground-state entanglement in the XXZ model, Phys. Rev. A , 2005,71: 052322.
[7]Alberto Anfossi,Paolo Giorda.Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions[J].Phys. Rev. Lett,2005,95:056402.
[8] Gu Shi-Jian.Entanglement and Quantum Phase Transition in the Extended Hubbard Model[J]. Phys. Rev. Lett, 2004, 93:086402. [16] Liang Shaorong , Liu Changnian.Calorifics ([M]. Beijing：Higher Education Press,2006, 147. (in Chinese).
[9] 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, 2008,77: 034303.
[10] Cao Min，Zhu Shiqun .Thermal Entanglement between Alternate Qubits of a Four-qubit Heisenberg XX Chain in a Magnetic Field[J].Phys. Rev. A，2005，71：034311.
[11]Wang Xiaoguang.Thermal and ground-state entanglement in Heisenberg XX qubit rings[J].Phys. Rev. A, 2002，66：034302.
[12] Hao Xiang, Zhu Shiqun. Entanglement in a spin-s antiferromagnetic Heisenberg chain[J]. Phys. Rev. A , 2005,72: 042306.
[13] Wang Xiaoguang . Boundary and impurity effects on the entanglement of Heisenberg chains[J]. Phys. Rev.E, 2004,69:066118.
[14] Amico Luigi .Entanglement in Many-body Systems[J].Rev. Mod. Phys, 2008, 80: 517.
[15] Wang Xiaoguang . Entanglement in the quantum Heisenberg XY model[J].Phys. Rev. A, 2001, 64: 012313.
[16] Pan Feng ,Liu Dan,LU Guoying.Recent progress on entanglement of multipartite pure state [J]. Journal of Liaoning Normal University (Natural Science) 辽宁师范大学学报(自然科学版),2003,26(4):364-367(in Chinese).
[17] Pan Feng. Permutation group approach to the one-dimrnsional XXX heisenberg open spin-1/2 chains[J]. International Journal of Modern Physics,2004,C15:247-265.