海森堡模型中概率及相应熵的计算分析

J4 ›› 2012, Vol. 29 ›› Issue (4): 427-433.

海森堡模型中概率及相应熵的计算分析

韩文娟, 周勋, 张太荣

1 贵州省六盘水师范学院物理与电子科学系, 贵州六盘水 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:2011-09-20 修回日期:2012-01-06 出版日期:2012-07-28 发布日期:2012-07-01
通讯作者: 韩文娟（1975-），女，河北保定人，副教授,从事量子多体理论的研究。 E-mail:hanwenjuanying@163.com
基金资助:
贵州六盘水科技基金资助(52020 －2009 － 08 ---01)、贵州六盘水师范学院科研项目基金资助(200906)

Calculation and analysis of probability and corresponding entropy of Heisenberg model

HAN Wen-juan, ZHOU Xun, ZHANG Tairong

1 Department of Physics and Electronics of Sciences, Guizhou Liupanshui Normal College, Liupanshui 553004,China;
2 School of Physics and Electronics, Guizhou Normal University,Guiyang 550001, China

Received:2011-09-20 Revised:2012-01-06 Published:2012-07-28 Online:2012-07-01

摘要/Abstract

摘要：

介绍海森堡模型的不同位型[N，n] （N为海森堡链总格点数, n为格点中自旋向下的电子数）中的体现本征值获取难易程度的本征值获取概率及其相应信息熵（香农所定义的）和体现模型体系关联程度的自旋向下电子发现概率、每一粒子的von Neumann及体系的平均von Neumann熵，可为量子计算与信息传递提供启示性信息。研究结果：(1)事件发生概率大于（小于）50%时，信息熵随概率增加而减小（增加）。(2)不同位型[N，n]，当n（N）同, N（n）增加时：本征值获取概率减小,其相应的信息熵正确反映本征值获取的难易程度；模型参数一定时，格点中自旋向下电子发现概率与每一粒子的von Neumann及体系的平均von Neumann熵都分别减小（增加）。(3)位型[N，n]相同时, 每一粒子的von Neumann及体系的平均von Neumann熵随参数变化时出现拐点,显示体系发生量子相变的信息。(4)同位型[N，n]且同参数时处于海森堡链对称位置粒子的von Neumann熵相同。

关键词: 量子光学, 概率, 信息熵, von Neumann熵, 海森堡模型, 电子自旋

Abstract:

In the situation of [N，n]( N is the total number of sites of heisenberg chain , n is the number of electrons at site spin down)of heisenberg model,The acquisition probability of the eigenvalues and the corresponding information entropy definited by Xiang Nong (They can embody the obtaining difficulty of the eigenvalue )are showed firstly, then the finding probability of site electron spin down , the von Neumann of each particle and average von Neumann entropy of the model system (They can embody the relevancy extent of model system) are talked.The studying results are the following.(1)When the probability of event occurrence is more (less) than 50%, the information entropy decreases(increases) along with the increase of the probability.(2) When n (N) is same and N (n) increases,the acquisition probability of the eigenvalues of [N, n] decreases.The corresponding information entropy correctly reflects the obtaining difficulty of the eigenvalue；When n (N) is same , N (n) increases and the parameter is fixed, the finding probability of site electron spin down , the von Neumann of each particle and average von Neumann entropy of the model system decrease(increase) respectively.(3) When [N，n] is same, the von Neumann of each particle and average von Neumann entropy of the model system change along with the change of the parameter ,the points of inflection arise.These can embody the information of the quantum phase transition of the system . (4) When [N，n] and the parameter are same , the von Neumann of the particles of the symmetric position of heisenberg chain is same.

Key words: quantum optics, probability, information entropy, von Neumann entropy, Heisenberg model, electron spin

中图分类号:

O431.2

韩文娟, 周勋, 张太荣 . 海森堡模型中概率及相应熵的计算分析[J]. J4, 2012, 29(4): 427-433.

HAN Wen-juan, ZHOU Xun, ZHANG Tairong. Calculation and analysis of probability and corresponding entropy of Heisenberg model[J]. J4, 2012, 29(4): 427-433.

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