Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

Physical Review B - Condensed Matter and Materials Physics

Volumn 60, Issue 17, 1999, Pages 12116-12124

  Furusaki, A ^b   Sigrist, M ^b  

^a KOBE UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001388966     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.60.12116     Document Type: Article

References (40)

1. S.-k. Ma, C. Dasgupta, and C.-k. Hu, Phys. Rev. Lett. 43, 1434 (1979);
2. C. Dasgupta and S.-k. Ma, Phys. Rev. B 22, 1305 (1980).
3. D. S. Fisher, Phys. Rev. B 50, 3799 (1994).
4. R. A. Hyman, Kun Yang, R. N. Bhatt, and S. M. Girvin, Phys. Rev. Lett. 76, 839 (1996);
5. Phys. Rev. Lett.R. A. Hyman and Kun Yang, 78, 1783 (1997);
6. Phys. Rev. Lett.Kun Yang and R. N. Bhatt, 80, 4562 (1998).
7. M. Fabrizio and R. Mélin, Phys. Rev. Lett. 78, 3382 (1997).
8. C. Monthus, O. Golinelli, and Th. Jolicoeur, Phys. Rev. Lett. 79, 3254 (1997).
9. L. N. Bulaevskii, A. V. Zvarykina, Yu. S. Karimov, R. B. Lyuubovskii, and I. F. Shchegolev, Zh. Éksp. Teor. Fiz. 62, 725 (1972) [Sov. Phys. JETP 35, 384 (1972)];
10. L. J. Azevedo and W. G. Clark, Phys. Rev. B 16, 3252 (1977).
11. G. Theodorou and M. H. Cohen, Phys. Rev. Lett. 37, 1014 (1976);
12. G. Theodorou, Phys. Rev. B 16, 2264 (1977);
13. Phys. Rev. BG. Theodorou16, 2273 (1977).
14. T. N. Nguyen, P. A. Lee, and H.-C. zur Loye, Science 271, 489 (1996).
15. A. Furusaki, M. Sigrist, P. A. Lee, K. Tanaka, and N. Nagaosa, Phys. Rev. Lett. 73, 2622 (1994);
16. A. Furusaki, M. Sigrist, E. Westerberg, P. A. Lee, K. B. Tanaka, and N. Nagaosa, Phys. Rev. B 52, 15 930 (1995).
17. M. Azuma, Y. Fujishiro, M. Takano, M. Nohara, and H. Takagi, Phys. Rev. B 55, R8658 (1997);
18. M. Azuma, M. Takano, and R. S. Eccleston, J. Phys. Soc. Jpn. 67, 740 (1998).
19. Y. Motome, N. Katoh, N. Furukawa, and M. Imada, J. Phys. Soc. Jpn. 65, 1949 (1996);
20. J. Phys. Soc. Jpn.Y. Iino and M. Imada, 65, 3728 (1996).
21. H. Fukuyama, N. Nagaosa, M. Saito, and T. Tanimoto, J. Phys. Soc. Jpn. 65, 2377 (1996).
22. M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996);
23. J. Phys. Soc. Jpn.N. Nagaosa, A. Furusaki, M. Sigrist, and H. Fukuyama, 65, 3724 (1996).
24. G. B. Martins, E. Dagotto, and J. A. Riera, Phys. Rev. B 54, 16 032 (1996).
25. H.-J. Mikeska, U. Neugebauer, and U. Schollwöck, Phys. Rev. B 55, 2955 (1997).
26. T. Miyazaki, M. Troyer, M. Ogata, K. Ueda, and D. Yoshioka, J. Phys. Soc. Jpn. 66, 2580 (1997).
27. M. Greven and R. J. Birgeneau, Phys. Rev. Lett. 81, 1945 (1998).
28. P. Henelius and S. M. Girvin, Phys. Rev. B 57, 11 457 (1998).
29. E. Westerberg, A. Furusaki, M. Sigrist, and P. A. Lee, Phys. Rev. Lett. 75, 4302 (1995);
30. E. WesterbergA. FurusakiM. SigristP. A. LeePhys. Rev. B 55, 12 578 (1997).
31. B. Frischmuth and M. Sigrist, Phys. Rev. Lett. 79, 147 (1997);
32. B. Frischmuth, M. Troyer, B. Ammon, and M. Sigrist, Phys. Rev. B 60, 3388 (1999).
33. See, for example, J. J. Sakurai, Modern Quantum Mechanics (Benjamin/Cummings, Menlo Park, 1985), p. 238.
34. S. R. White, Phys. Rev. Lett. 69, 2863 (1992);
35. S. R. WhitePhys. Rev. B 48, 10 345 (1993).
36. S. R. White, Phys. Rev. Lett. 77, 3633 (1996).
37. K. Hida, J. Phys. Soc. Jpn. 66, 330 (1997).
38. A. P. Young and H. Rieger, Phys. Rev. B 53, 8486 (1996).
39. We also tried the stretched exponential form, (Formula presented), with which we could fit the numerical data as well as with Eq. (18). Here (Formula presented), and (Formula presented) are constants.
40. Some data points at (Formula presented) are off the scaling curve in Fig. 77. We estimate that the numerical error in (Formula presented) in our calculation is of order (Formula presented). The scattered data are those with small correlations of order (Formula presented). Thus the failure of the data collapse at (Formula presented) does not mean the violation of the scaling.