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Prog. Theor. Phys. Vol. 74 No. 3 (1985) pp. 468-478

[ Full Text PDF : FREE ACCESS (506K) ]

The Ground-State Energy of the Heisenberg Antiferromagnet with Anisotropic Exchange Interaction

Satoru J. Miyake

Department of Physics, Tokyo Institute of Technology, Tokyo 152.

(Received March 30, 1985)

Abstract:

The ground-state energy of the Heisenberg antiferromagnet with the XY-like anisotropy is examined with the use of a revised form of the Holstein-Primakoff transformation. The energy is calculated perturbationally with 1/S as an expansion parameter, S being the magnitude of spin. The contribution from the kinematical interaction of spin waves is shown to be of the order of exp (-aS) (a>0) except for the linear chain, and accordingly negligible in the asymptotic expansion in 1/S. The obtained ground-state energy agrees up to 1/S2 with that obtained ealier for bipartite lattices. For non-bipartite lattices, there is an extra term of O(1/S2) which has not been considered hitherto. The coefficient of the order 1/S2 for the triangular lattice is calculated numerically.


URL : http://ptp.ipap.jp/link?PTP/74/468/
DOI : 10.1143/PTP.74.468

[ Full Text PDF : FREE ACCESS (506K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 3648-3651 :
    Excitation in Antiferromagnetic Quantum Spin Systems on the Triangular Lattice
    Tosizumi Aoki
  2. Journal of the Physical Society of Japan 57 (1988) pp. 626-638 :
    Ground State of Quantum Spin Systems on the Triangular Lattice
    Hidetoshi Nishimori and Hiizu Nakanishi
  3. Journal of the Physical Society of Japan 60 (1991) pp. 614-624 :
    Boson Mean Field Theory of the Triangular Lattice Heisenberg Model
    Daijiro Yoshioka and Jun Miyazaki
  4. Journal of the Physical Society of Japan 61 (1992) pp. 3732-3744 :
    Ground-State Properties and Phase Diagram of the Quantum XXZ Antiferromagnet on a Triangular Lattice
    Tsutomu Momoi and Masuo Suzuki
  5. Journal of the Physical Society of Japan 62 (1993) pp. 880-887 :
    Thermodynamic Properties of Antiferromagnetic Quantum XY-Model on the Triangular Lattice
    Shigeo Homma, Hirotsugu Matsuda, Naofumi Ogita and Kazuhiro Sano
  6. Journal of the Physical Society of Japan 65 (1996) pp. 569-580 :
    Thermodynamic Properties of the Square Lattice XXZ Model: A Schwinger Boson Mean-Field Theory
    Yoshiyuki Fukumoto
  7. Journal of the Physical Society of Japan 70 (2001) pp. 954-960 :
    Kinematical Interaction between S=1/2 Spins in the Two-time Spin Green's Function Method
    Tosizumi Aoki
  8. Progress of Theoretical Physics Vol. 77 No. 2 (1987) pp. 287-296 :
    Quantum Monte Carlo Simulation of Antiferromagnetic Heisenberg Model on the Triangular Lattice
    Kazuhiro Sano
  9. Progress of Theoretical Physics Supplement No.87 (1986) pp. 127-138 :
    Decoupled Cell Monte Carlo Method for Quantum Spin Systems on Linear Chain and on Triangular Lattice
    Shigeo Homma, Kazuhiro Sano, Hirotsugu Matsuda and Naofumi Ogita

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