关于海森堡模型中一种并行算法实现的讨论

J4 ›› 2014, Vol. 31 ›› Issue (1): 80-85.

关于海森堡模型中一种并行算法实现的讨论

黄敏¹,韩文娟²,刘海²

1 贵州省六盘水师范学院数学系, 贵州六盘水 553004； 2 贵州省六盘水师范学院物理与电子科学系, 贵州六盘水 553004； 3 贵州省六盘水师范学院物理与电子科学系, 贵州六盘水 553004

收稿日期:2013-07-10 修回日期:2013-08-27 出版日期:2014-01-28 发布日期:2013-12-31
作者简介:黄敏（1973-）苗族，贵州道真人，硕士，副教授，研究方向：数学与计算机教学与研究.Email地址：lpsszhm@163.com

Discussion on implementation of a parallel algorithm about Heisenberg mode

HUANG Min, HAN Wen-juan, LIU Hai

1 Department of Mathematics,Guizhou Liupanshui Normal College, Liupanshui 553004,China; 2 Department of Physics and Electronics of Sciences, Guizhou Liupanshui Normal College, Liupanshui 553004,China; 3 Department of Physics and Electronics of Sciences,Guizhou Liupanshui Normal College, Liupanshui 553004,China

Received:2013-07-10 Revised:2013-08-27 Published:2014-01-28 Online:2013-12-31

摘要/Abstract

摘要： 使用并行算法（简称Z分法）fortran编程计算获取海森堡模型位型[N，k] （N为海森堡链总格点数, k为格点中自旋向上的电子数）的最小本征值的最短时间。研究方法：使用置换群方法产生模型的能量矩阵，将能量矩阵对角化所得到的本征值构成数据群，采用Z（Z=1,2……）分法Fortran编程计算获得群中最小数据的最短(或最长)时间。研究结论：(1）同一位型[N,k]，使用2分法获取模型位型[N，k]的最小本征值的时间最长，而不等分或满等分（此时Z=1或位型[N，k]的矩阵维数）时的时间最短且二者相等。(2）对于不同位型[N,k] ，Z相同而当N（k）同,k（N）增大时，获取模型最小本征值的最短时间增加。通过讨论海森堡模型获取最小本征值的时间计量可为研究者们在计算工作中作提高运算效率的借鉴。

关键词: 量子光学, 并行算法, 本征值, 海森堡模型, 时间

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

中图分类号:

O431.2

黄敏韩文娟刘海. 关于海森堡模型中一种并行算法实现的讨论[J]. J4, 2014, 31(1): 80-85.

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

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