Recent developments of world-line Monte Carlo methods

Journal of the Physical Society of Japan

Volumn 73, Issue 6, 2004, Pages 1379-1414

  Kawashima, Naoki ^a   Harada, Kenji ^b  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Cluster algorithm; Directed loop algorithm; Heisenberg model; Loop algorithm; Quantum Monte Carlo; Quantum spin system; World line method; Worm algorithm; XXZ model; XY model

Indexed keywords

ALGORITHM; CALCULATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MONTE CARLO METHOD; QUANTUM MECHANICS; REVIEW;

EID: 11844303116     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.73.1379     Document Type: Review

References (68)

1. M. Suzuki: Prog. Theor. Phys. 56 (1976) 1454.
2. H. G. Evertz, G. Lana and M. Marcu: Phys. Rev. Lett. 70 (1993) 875.
3. N. V. Prokov'ev, B. V. Svistunov and I. S. Tupitsyn: Sov. Phys. JETP 87 (1998) 310.
4. O. F. Syljuåsen and A. W. Sandvik: Phys. Rev. E 66 (2002) 046701.
5. N. Kawashima and J. E. Gubernatis: Phys. Rev. Lett. 73 (1994) 1295.
6. A. W. Sandvik: Phys. Rev. B 59 (1999) 14157.
7. B. B. Beard and U.-J. Wiese: Phys. Rev. Lett. 77 (1996) 5130.
8. R. Brower, S. Chandrasekharan and U.-W. Wiese: Physica A 261 (1998) 520.
9. V. A. Kashumikov, N. V. Prokofev, B. V. Svistunov and M. Troyer: Phys. Rev. B 59 (1999) 1162.
10. S. Chandrasekharan and U.-J. Wiese: Phys. Rev. Lett. 83 (1999) 3116.
11. S. Chandrasekharan, J. Cox, J. C. Osborn and U.-J. Wiese: Nucl. Phys. B 673 (2003) 405, and the references cited therein.
12. N. Hatano and M. Suzuki: in Quantum Monte Carlo Methods in Condensed Matter Physics, ed. M. Suzuki (World Scientific, Singapore, 1994) p. 13.
13. H. G. Evertz: Adv. Phys. 52 (2003) 1.
14. R. H. Swendsen and J.-S. Wang: Phys. Rev. Lett. 58 (1987) 86.
15. N. Kawashima and J. E. Gubernatis: Phys. Rev. E 51 (1995) 1547.
16. U. Wolff: Phys. Rev. Lett. 62 (1989) 361.
17. D. Kandel and E. Domany: Phys. Rev. B 43 (1991) 8539.
18. N. Kawashima and J. E. Gubernatis: J. Stat. Phys. 80 (1995) 169.
19. P. W. Kasteleyn and C. M. Fortuin: J. Phys. Soc. Jpn. 26 (1969) Suppl., p. 11.
20. C. M. Fortuin and P. W. Kasteleyn: Physica 57 (1972) 536.
21. D. C. Handscomb: Proc. Cambridge Philos. Soc. 58 (1962) 594;
22. D. C. Handscomb: Proc. Cambridge Philos. Soc. ibid. 60 (1964) 115.
23. M. Suzuki, S. Miyashita and A. Kuroda: Prog. Theor. Phys. 58 (1977) 1377.
24. M. Marcu: in Quantum Monte Carlo Methods in Equilibrium and Non-Equilibrium Systems, ed. M. Suzuki (Springer-Verlag, Berlin, 1987) p. 64.
25. A. Wiesler: Phys. Lett. A 89 (1982) 359.
26. T. Nakamura and Y. Ito: J. Phys. Soc. Jpn. 72 (2003) 2405.
27. H. G. Evertz and M. Marcu: in Quantum Monte Carlo Methods in Condensed Matter Physics, ed. M. Suzuki (World Scientific, Singapore, 1994) p. 65.
28. M. Aizenman and B. Nachtergaele: Commun. Math. Phys. 164 (1994) 17.
29. N. Kawashima: J. Stat. Phys. 82 (1996) 131.
30. K. Harada and N. Kawashima: J. Phys. Soc. Jpn. 70 (2001) 13.
31. M. S. Makivic and K.-Q. Ding: Phys. Rev. B 43 (1991) 3562.
32. A sample program based on the directed loop algorithm (with the solution obtained by the coarse-graining technique) may be found in http://ccmp18.phys. metro-u.ac.jp/QMC
33. K. Harada and N. Kawashima: Phys. Rev. B 55 (1997) R11949.
34. K. Harada and N. Kawashima: J. Phys. Soc. Jpn. 67 (1998) 2768.
35. D. R. Nelson and J. M. Kosterlitz: Phys. Rev. Lett. 39 (1977) 1201.
36. E. L. Pollock and D. M. Ceperley: Phys. Rev. B 36 (1987) 8343.
37. M. Marcu and A. Wiesler: J. Phys. A 18 (1985) 2479.
38. N. Hatano: J. Phys. Soc. Jpn. 64 (1995) 1529.
39. A. W. Sandvik and J. Kurkijärvi: Phys. Rev. B 43 (1991) 5950.
40. A. W. Sandvik: J. Phys. A 25 (1992) 3667.
41. K. Harada, M. Troyer and N. Kawashima: J. Phys. Soc. Jpn. 67 (1998) 1130.
42. S. Todo and K. Kato: Phys. Rev. Lett. 87 (2001) 047203.
43. For physical results on this model, see, for example, A. Schmitt, K. H. Mütter, M. Karbach, Y. Yu and G. Müller: Phys. Rev. B 58 (1998) 5498, and references cited therein;
44. also see K. Nomura and S. Takada: J. Phys. Soc. Jpn. 60 (1991) 389.
45. K. Harada and N. Kawashima: Phys. Rev. E 66 (2002) 056705;
46. K. Harada and N. Kawashima: Phys. Rev. E ibid. 67 (2003) 039903(E).
47. K. Harada, N. Kawashima and M. Troyer: Phys. Rev. Lett. 90 (2003) 117203.
48. 43) we used the same word to refer to the head or the tail, individually, because only these two points are the essential ingredients of the algorithm. 'The two-ladybug algorithm' might be a more appropreate name of the algorithm.
49. F. Alet, S. Wessel and M. Troyer: cond-mat/0308495.
50. J. Smakov, K. Harada and N. Kawashima: Phys. Rev. E 68 (2003) 046708.
51. J. Holstein and N. Primakoff: Phys. Rev. 58 (1940) 1098.
52. N. Hatano and M. Suzuki: Phys. Lett. A 163 (1992) 246.
53. H. G. Evertz and W. von der Linden: Phys. Rev. Lett. 86 (2001) 5164.
54. B. A. Berg and T. Neuhaus: Phys. Lett. B 267 (1991) 249.
55. B. A. Berg and T. Neuhaus: Phys. Rev. Lett. 68 (1992) 9.
56. J. Lee: Phys. Rev. Lett. 71 (1993) 211.
57. F. Wang and D. P. Landau: Phys. Rev. Lett. 86 (2001) 2050.
58. C. Yamaguchi and N. Kawashima: Phys. Rev. E 65 (2002) 056710.
59. M. Troyer, S. Wessel and F. Alet: Phys. Rev. Lett. 90 (2003) 120201.
60. C. Yamaguchi, N. Kawashima and Y. Okabe: Phys. Rev. E 66 (2002) 036704.
61. W. Janke and S. Kappler: Phys. Rev. Lett. 74 (1995) 212.
62. P. M. C. de Oliveira, T. J. P. Penna and H. J. Herrmann: Braz. J. Phys. 26 (1998) 677;
63. Eur. Phys. J. B 1 (1998) 205.
64. J.-S. Wang, T. K. Tay and R. H. Swendsen: Phys. Rev. Lett. 82 (1999) 476.
65. C. Yamaguchi, N. Kawashima and Y. Okabe: unpublished.
66. H. Rieger and N. Kawashima: Eur. Phys. J. B 9 (1999) 233.
67. A. Dorneich and M. Troyer: Phys. Rev. E 64 (2001) 066701.
68. K. Harada and N. Kawashima: unpublished.