• Chinese Journal of Quantum Electronics
  • Vol. 29, Issue 4, 427 (2012)
Wen-juan HAN1、*, Xun ZHOU2, and Tai-rong ZHANG1
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
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    DOI: 10.3969/j.issn.1007-5461. 2012.04.008 Cite this Article
    HAN Wen-juan, ZHOU Xun, ZHANG Tai-rong. Calculation and analysis of probability and corresponding entropy of Heisenberg model[J]. Chinese Journal of Quantum Electronics, 2012, 29(4): 427 Copy Citation Text show less

    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 eigenvalues and corresponding information entropy definited by Shannon 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 discussed. 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 entropy of each particle and average von Neumann entropy of the model system decrease(increase) respectively. 3) When [N,n] is same, the von Neumann entropy 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 entropy of the particles of symmetric position of Heisenberg chain is same.
    HAN Wen-juan, ZHOU Xun, ZHANG Tai-rong. Calculation and analysis of probability and corresponding entropy of Heisenberg model[J]. Chinese Journal of Quantum Electronics, 2012, 29(4): 427
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