Prog. Theor. Phys. Vol. 75 No. 4 (1986) pp. 808-827
Study of One-Dimensional Quantum Spin Systems by the Transger-Matrix Method. II
— S=1 Case
Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11
(Received November 25, 1985)
The one-dimensional S=1 quantum spin system has been mapped onto the equivalent two-dimensional Ising model on the basis of the equivalence theorem of Suzuki. The classical representation of the partition function has been expressed in terms of the maximum eigenvalue of the transfer matrix and evaluated by means of the numerically exact transfer-matrix method. The physical meaning of two kinds of correlation functions in RSD and CBD has been made clear in terms of the concept of the maximum eigenstate. Calculations have been made for both ferromagnetic and antiferromagnetic Heisenberg chains with several single-site anisotropy values, both positive and negative. Good agreements are found with some existing numerical results.
DOI : 10.1143/PTP.75.808
H. A. Kramers and G. H. Wannier, Phys. Rev. 60 (1941), 252[APS].
H. Betsuyaku, Phys. Rev. Lett. 53 (1984), 629[APS]; Prog. Theor. Phys. 73 (1985), 319[PTP]. These articles will be reffered to as I hereafter.
M. Suzuki, Phys. Rev. B31 (1985), 2597[APS].
- T. Tsuzuki, Prog. Theor. Phys. 73 (1985), 1352[PTP]; ibid. 75 (1986), 225[PTP].
T. Sakaguchi, K. Kubo and S. Takada, J. Phys. Soc. Jpn. 54 (1985), 861[JPSJ].
- T. Yokota and H. Betsuyaku, Prog. Theor. Phys. 75 (1986), 46[PTP]. This article will be referred to as II hereafter.
- H. Betsuyaku and T. Yokota, Phys. Rev. B33 (1986), No. 9.
- H. Betsuyaku, Prog. Theor. Phys. 75 (1986), 774[PTP].
- M. Suzuki, Prog. Theor. Phys. 56 (1976), 1454[PTP].
- M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys. 58 (1977), 1377[PTP].
M. Barma and B. S. Shastry, Phys. Rev. B18 (1978), 3351[APS].
- H. W. J. Blöte, Physica 79B (1975), 427.
- H. Betsuyaku, unpublished.
R. Blackenbecler and R. L. Suger, Phys. Rev. D27 (1983), 1304[APS].
- H. De Raedt, A. Lagendijk and J. Fivez, Z. Phys. B46 (1982), 261.
- M. Kolb, R. Botet and R. Jullien, J. of Phys. A16 (1983), L673, and references therein.
- M. Steiner, J. Villain and G. G. Windsor, Adv. Phys. 25 (1976), 87.
A. P. Ramirez and W. P. Wolf, Phys. Rev. Lett. 49 (1982), 227[APS].
Citing Article(s) :
Journal of the Physical Society of Japan 56 (1987) pp. 1963-1973
Cluster-Spin Quantum Monte Carlo Study of One-Dimensional Heisenberg Model
Yutaka Okabe and Macoto Kikuchi
Journal of the Physical Society of Japan 62 (1993) pp. 1459-1462
Thermodynamic Properties of S=1 Antiferromagnetic Heisenberg Chains
Seiji Miyashita and Shoji Yamamoto
Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 30-38
On the Convergence of the Trotter-Like Formula and the Finite-Trotter-Number Scaling Law in the Transverse Ising Chain
Makoto Inoue and Masuo Suzuki