Crossover effects in the random-exchange spin-1/2 antiferromagnetic chain

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 5, 2004, Pages

  Laflorencie, Nicolas ^a   Rieger, Heiko ^b   Sandvik, Anders W ^c   Henelius, Patrik ^d  

^a CNRS   (France)

^b SAARLAND UNIVERSITY   (Germany)

^c ÅBO AKADEMI UNIVERSITY   (Finland)

^d ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ANALYTICAL ERROR; ARTICLE; CALCULATION; CORRELATION FUNCTION; MAGNETIC FIELD; QUANTUM MECHANICS; STOCHASTIC MODEL;

EID: 37649028023     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.054430     Document Type: Article

References (50)

1. H. Bethe, Z. Phys. 38, 441 (1931).
2. K. Hallberg, X. Q. G. Wang, P. Horsch, and A. Moreo, Phys. Rev. Lett. 76, 4955 (1996).
3. F. D. M. Haldane, Phys. Lett. 93A, 464 (1983).
4. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
5. F. Igloi, R. Juhász, and H. Rieger, Phys. Rev. B 61, 11552 (2000).
6. C. Doty and D. S. Fisher, Phys. Rev. B 45, 2167 (1992).
7. D. S. Fisher, Phys. Rev. B 50, 3799 (1994).
8. G. Refael, S. Kehrein, and D. S. Fisher, Phys. Rev. B 66, 060402(R) (2002); K. Damle and D. Huse, Phys. Rev. Lett. 89, 277203 (2002); E. Carlon et al., Phys. Rev. B 69, 144416 (2004).
9. G. Refael, S. Kehrein, and D. S. Fisher, Phys. Rev. B 66, 060402(R) (2002); K. Damle and D. Huse, Phys. Rev. Lett. 89, 277203 (2002); E. Carlon et al., Phys. Rev. B 69, 144416 (2004).
10. G. Refael, S. Kehrein, and D. S. Fisher, Phys. Rev. B 66, 060402(R) (2002); K. Damle and D. Huse, Phys. Rev. Lett. 89, 277203 (2002); E. Carlon et al., Phys. Rev. B 69, 144416 (2004).
11. K. Hida, Phys. Rev. Lett. 83, 3297 (1999); K. Yang and R. A. Hyman, ibid. 84, 2044 (2000); A. Saguia et al., ibid. 89, 117202 (2002).
12. K. Hida, Phys. Rev. Lett. 83, 3297 (1999); K. Yang and R. A. Hyman, ibid. 84, 2044 (2000); A. Saguia et al., ibid. 89, 117202 (2002).
13. K. Hida, Phys. Rev. Lett. 83, 3297 (1999); K. Yang and R. A. Hyman, ibid. 84, 2044 (2000); A. Saguia et al., ibid. 89, 117202 (2002).
14. S. Bergkvist, P. Henelius, and A. Rosengren, Phys. Rev. B 66, 134407 (2002).
15. S. K. Ma, C. Dasgupta, and C.-K. Hu, Phys. Rev. Lett. 43, 1434 (1979); C. Dasgupta and S.-K. Ma, Phys. Rev. B 22, 1305 (1980).
16. S. K. Ma, C. Dasgupta, and C.-K. Hu, Phys. Rev. Lett. 43, 1434 (1979); C. Dasgupta and S.-K. Ma, Phys. Rev. B 22, 1305 (1980).
17. S. Haas, J. Riera, and E. Dagotto, Phys. Rev. B 48, 13 174 (1993).
18. P. Henelius and S. M. Girvin, Phys. Rev. B 57, 11 457 (1998).
19. max= 128 spins), see Ref. 15.
20. A. P. Young and H. Rieger, Phys. Rev. B 53, 8486 (1996).
21. T. Hikihara, A. Furusaki, and M. Sigrist, Phys. Rev. B 60, 12 116 (1999).
22. S. Todo, K. Kato, and H. Takayama, in Computer Simulation Studies in Condensed-Matter Physics XI (Springer-Verlag, Berlin, 1999), pp. 57-61.
23. K. Harnacher, J. Stolze, and W. Wenzel, Phys. Rev. Lett. 89, 127202 (2002).
24. N. Laflorencie and H. Rieger, Phys. Rev. Lett. 91, 229701 (2003).
25. H. Röder, J. Stolze, R. Silver, and G. Müller, J. Appl. Phys. 79, 4632 (1996).
26. T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988).
27. D. S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).
28. D. S. Fisher, Phys. Rev. Lett. 69, 534 (1992); Phys. Rev. B 51, 6411 (1995).
29. For a review on Luttinger liquid, see H. J. Shulz, G. Cuniberti, and P. Pieri, Fermi Liquids and Luttinger Liquids, in Field Theories for Low-Dimensional Condensed Matter Systems (Springer, New York, 2000).
30. E. Orignac (private communication).
31. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
32. G. Bouzerar, D. Poilblanc, and G. Montambaux, Phys. Rev. B 49, 8258 (1994).
33. K. J. Runge and G. T. Zimanyi, Phys. Rev. B 49, 15 212 (1994).
34. L. Urba and A. Rosengren, Phys. Rev. B 67, 104406 (2003); in this study, DMRG calculations have been performed-on system up to 50 sites.
35. N. Laflorencie and H. Rieger, Eur. Phys. J. B 40, 201 (2004).
36. E. Lieb, T. Schulz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961).
37. For a study of dynamics and transport properties at nonzero frequency in random spin chains, see O. Montrunich, K. Damle, and D. Huse, Phys. Rev. B 63, 134424 (2001).
38. ±iφ
39. M. Wallin, E. S. Sørensen, S. M. Girvin, and A. P. Young, Phys. Rev. B 49 12 115 (1994).
40. -2, see N. Laflorencie, S. Capponi, and E. S. Sørensen, Eur. Phys. J. B 24, 77 (2001).
41. φ) whereas the evaluation of the mid-chain spin-spin correlation function requires to solve eigenvalues and eigenvectors problem on an L X L matrix and then requires us to calculate an (L/2) X (L/2) determinant.
42. A. W. Sandvik, Phys. Rev. B 59, R14 157 (1999).
43. O. F Syljuasen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002).
44. O. F Syljuasen, Phys. Rev. E 67, 046701 (2003).
45. F Alet, S. Wessel, and M. Troyer, cond-mat/0308495 (unpublished).
46. A. W. Sandvik, Phys. Rev. B 66, 024418 (2002).
47. N. Laflorencie, D. Poilblanc, and A. W. Sandvik, Phys. Rev. B 69, 212412 (2004).
48. S. Todo (private communication).
49. L. Affleck, D. Gepner, H. J. Schulz, and T. Ziman, J. Phys. A 22, 511 (1989).
50. 0) in order to get c̄(x) → 1 when x → 0.