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Prog. Theor. Phys. Vol. 73 No. 1 (1985) pp. 18-31

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Ground-State Energy of the Heisenberg Model with XY-Like Anisotropy

Hidetoshi Nishimori and Satoru J. Miyake

Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152

(Received October 15, 1984)

Abstract:

We estimate the ground-state energy of the quantum Heisenberg model with XY-like anisotropy on various lattices by a self-consistent harmonic approximation and by an expansion from the classical limit in powers of 1/S. A spin wave theory due to Villain gives the first order term in 1/S and the second order correction is obtained from the iterative solution of equations in the self-consistent harmonic approximation. Our coefficient of the second order term is not exact but we have reasons to believe that it is quite accurate. The second order expansion yields excellent values when comparison is possible with other exact and approximate estimates while the self-consistent harmonic approximation does not always work well. Our methods have the advantage of wide range of applicability and simplicity of the basic physical picture.


URL : http://ptp.ipap.jp/link?PTP/73/18/
DOI : 10.1143/PTP.73.18

[ Full Text PDF : OPEN SELECT (687K) ] Citation:

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  16. Journal of the Physical Society of Japan 63 (1994) pp. 2507-2510 :
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  17. Journal of the Physical Society of Japan 65 (1996) pp. 594-600 :
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  18. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1577-1579 :
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  19. Progress of Theoretical Physics Vol. 74 No. 3 (1985) pp. 468-478 :
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  20. Progress of Theoretical Physics Vol. 77 No. 2 (1987) pp. 287-296 :
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  21. Progress of Theoretical Physics Supplement No.87 (1986) pp. 127-138 :
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  22. Progress of Theoretical Physics Supplement No.101 (1990) pp. 391-402 :
    Absence of Chirality and Flux in Quantum Spin Systems and the Hubbard Model in Two-Dimension
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