Reexamination of finite-lattice extrapolation of Haldane gaps

Journal of the Physical Society of Japan

Volumn 78, Issue 1, 2009, Pages

  Nakano, Hiroki ^a   Terai, Akira ^b  

^a UNIVERSITY OF HYOGO   (Japan)

^b Osaka Prefecture University   (Japan)

Author keywords

Antiferromagnetic Heisenberg spin chain; Exact diagonalization method; Extrapolation; Haldane gap; Lanczos method

Indexed keywords

EID: 58549116502     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJ.78.014003     Document Type: Article

References (17)

1. F. D. Haldane: Phys. Rev. Lett. 50 (1983) 1153.
2. F. D. Haldane: Phys. Lett. A 93 (1983) 464.
3. Various estimates of the Haldane gap of S = 1 chain were extensively summarized in ref. 4. The case of S = 2 was given in Table I of ref. 12.
4. O. Golinelli, T. Jolicoeur, and R. Lacaze: Phys. Rev. B 50 (1994) 3037.
5. S. R. White and D. A. Huse: Phys. Rev. B 48 (1993) 3844.
6. S. Todo and K. Kato: Phys. Rev. Lett. 87 (2001) 047203.
7. A. Terai: presented at 19th IUPAP Int. Conf. Statistical Physics, 1995.
8. When system sizes are very small, the dimensions of the Hilbert space are also small; Lanczos calculations sometimes become unstable. In these cases, we perform the Householder diagonalizations instead.
9. P. Wynn: Numer. Math. 8 (1966) 264.
10. D. Shanks: J. Math. Phys. (Cambridge, Mass.) 34 (1955) 1.
11. T. Sakai and M. Takahashi: Phys. Rev. B 42 (1990) 1090.
12. X. Wang, S. Qin, and L. Yu: Phys. Rev. B 60 (1999) 14529.
13. -1/2log[S(S + 1)/Δ(S)] in this case, the analysis based on the same linear line (20) is available.
14. An example of a different model was reported in refs. 15 and 16.
15. H. Nakano and Y. Takahashi: J. Phys. Soc. Jpn. 73 (2004) 983.
16. H. Nakano, Y. Takahashi, and M. Imada: J. Phys. Soc. Jpn. 76 (2007) 034705.
17. C. Brezinski: J. Comput. Appl. Math. 122 (2000) 1.