Calculation and analysis of probability and corresponding entropy of Heisenberg model

Abstract

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

CLC Number:

O431.2

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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Calculation and analysis of probability and corresponding entropy of Heisenberg model

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