---

Prog. Theor. Phys. Supplement No.87 (1986) pp. 247-255

Numerical Diagonalization of Quantum Spin Hamiltonians

Hidetoshi Nishimori and Yoshihiro Taguchi

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

(Received June 14, 1986)

Abstract:

We explain numerical methods to calculate low-lying eigenstates of the finite-size spin-1/2 anisotropic Heisenberg model. Sparse matrix techniques and a bit representation of spin configurations are shown to be quite useful in writing a program independent of specific lattice structure. A few examples of application are presented to demonstrate the effectiveness of our method.

URL : http://ptp.ipap.jp/link?PTPS/87/247/
DOI : 10.1143/PTPS.87.247

[ Full Text PDF : FREE ACCESS (709K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. K. Binder and D. Stauffer, in Applications of the Monte Carlo Methods in Statistical Physics, ed. K. Binder, Topics in Current Physics 36 (Springer, Berlin, 1984), p. 1.
2. I. Morgenstern, in , ed. J. L. van Hemmen and I. Morgenstern, Lecture Notes in Physics 192 (Springer, Berlin, 1983), p. 305.
3. M. Suzuki, Phys. Rev. B 31 (1985), 2957[APS].
4. T. Oguchi and Y. Taguchi, Prog. Theor. Phys. Suppl. No. 87 (1986), 23[PTP].
5. J. C. Bonner and M. E. Fisher, Phys. Rev. 135 (1964), A640[APS].
6. T. Oguchi, H. Nishimori and Y. Taguchi, J. Phys. Soc. Jpn. 55 (1986), 323[JPSJ].
7. M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys. 58 (1977), 1377[PTP].
8. H. De Raedt and A. Lagendijk, Phys. Rep. 127 (1985), 233[CrossRef].
9. M. Takasu, S. Miyashita and M. Suzuki, Prog. Theor. Phys. 75 (1986), 1254, [PTP]and references therein.
10. H. Nishimori, Y. Taguchi and T. Oguchi, J. Phys. Soc. Jpn. 55 (1986), 656[JPSJ].
11. T. Oguchi, H. Nishimori and Y. Taguchi, J. Phys. Soc. Jpn. 54 (1985), 4494[JPSJ].
12. K. Okamoto, H. Nishimori and Y. Taguchi, J. Phys. Soc. Jpn. 55 (1986), 1458[JPSJ].
13. H. Nishimori and S. Miyashita, J. Phys. Soc. Jpn. 55 (1986), 4448[JPSJ].
14. R. R. Whitehead, A. Watt, B. J. Cole and I. Morrison, in Advances in Nuclear Physics Vol. 9, ed. M. Baranger and E. Vogt (Plenum, New York, 1977), p. 123.
15. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford, Oxford, 1965).
16. H. Togawa, Matrix no Suchi Keisan (Numerical Calculation of Matrices) (in Japanese) (Ohm-Sha, Tokyo, 1971).
17. E. R. Gagliano, E. Dagotto, A. Moreo and F. C. Alcaraz, Phys. Rev. B 34 (1986), 1677[APS].
18. M. R. Hestenes, in Proc. of Sixth Symposium in Applied Mathematics of AMS, Santa Monica, 1953, ed. J. H. Curtiss (McGraw-Hill, New York, 1956), p. 83.
19. J. W. Bray, L. V. Interrante, I. S. Jacobs and J. C. Bonner, in Extended Linear Chain Compounds Vol. 3, ed. J. S. Miller (Plenum, New York, 1983), p. 353.
20. P. W. Anderson, Mat. Res. Bull. 8 (1973), 153.
21. S. Miyashita, J. Phys. Soc. Jpn. 55 (1986), 3605[JPSJ].

Citing Article(s) :

1. Journal of the Physical Society of Japan 56 (1987) pp. 2153-2167 :

   Ground-State Properties of the One-Dimensional Isotropic Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions

   Takashi Tonegawa and Isao Harada

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 58 (1989) pp. 1403-1415 :

   Theory of the Resonating Valence Bond in Quantum Spin System

   Takehiko Oguchi and Hidetsugu Kitatani

4. Journal of the Physical Society of Japan 60 (1991) pp. 3449-3459 :

   Diagonalization Study of the Two-Impurity Anderson Model

   Takashi Yanagisawa

5. Progress of Theoretical Physics Vol. 79 No. 2 (1988) pp. 253-257 :

   Some Properties of Eigenvalues and Eigenfunctions for Finite Systems on the Antiferromagnetic Heisenberg Model

   Takehiko Oguchi and Hidetsugu Kitatani

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.