Quantum Monte Carlo in the interaction representation: Application to a spin-Peierls model

Physical Review B - Condensed Matter and Materials Physics

Volumn 56, Issue 22, 1997, Pages 14510-14528

  Sandvik, A ^a   Singh, R ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001709849     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.56.14510     Document Type: Article

References (62)

1. H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
2. M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
3. For reviews of QMC methods, see, e.g., D. Scalapino, in Frontiers and Borderlines in Many-Particle Physics, Proceedings of International School of Physics “Enrico Fermi, ” 1987, edited by R. A. Broglia and J. R. Schrieffer (Elsevier Science, Amsterdam, 1988).
4. W. Von Der Linden, Phys. Rep. 220, 53 (1992); A. W. Sandvik, in Strongly Correlated magnetic and Superconducting Systems, Proceedings of the 1996 El Escorial Summer School, edited by G. Sierra and M. A. Martin Delgado (Springer-Verlag, Berlin, 1997).
5. Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, edited by M. Suzuki (Springer-Verlag, Berlin, 1987).
6. M. Suzuki, S. Miyashita, and A. Kuroda, Prog. Theor. Phys. 58, 1377 (1977).
7. M. Barma and B. S. Shastry, Phys. Rev. B 18, 3351 (1977).
8. J. J. Cullen and D. P. Landau, 27, 297 (1983).
9. J. E. Hirsch, R. L. Sugar, D. J. Scalapino, and R. Blankenbecler, Phys. Rev. B 26, 5033 (1982).
10. R. M. Fye, Phys. Rev. B 33, 6271 (1986).
11. D. C. Handscomb, Proc. Cambridge Philos. Soc. 58, 594 (1962).
12. 60, 115 (1964).
13. Y. C. Chen, H. H. Chen, and F. Lee, Phys. Lett. A 130, 257 (1988).
14. J. W. Lyklema, Phys. Rev. Lett. 49, 88 (1982).
15. R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Phys. Rev. D 24, 2278 (1981).
16. D. H. Lee, J. D. Joannopoulos, and J. W. Negele, Phys. Rev. B 30, 1599 (1984).
17. S. C. Chakravarty and D. B. Stein, Phys. Rev. Lett. 49, 582 (1982).
18. M. Suzuki, in Quantum Monte Carlo Method in Equilibrium and Nonequilibrium Systems (Ref. 4), p. 2.
19. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Redwood City, California, 1988).
20. A. W. Sandvik and J. Kurkijärvi, Phys. Rev. B 43, 5950 (1991).
21. A. W. Sandvik, J. Phys. A 25, 3667 (1992).
22. N. V. Prokof’ev, B. V. Svistunov, and I. S. Tupitsyn, cond-mat/9703200 (unpublished).
23. Zh. Eksp. Teor. Fiz. 64, 853 (1996).
24. B. B. Beard and U.-J. Wiese, Phys. Rev. Lett. 77, 5130 (1996).
25. H. G. Evertz, G. Lana, and M. Marcu, Phys. Rev. Lett. 70, 875 (1993).
26. R.-H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987).
27. M. Hase, I. Terasaki, and K. Uchinokura, Phys. Rev. Lett. 70, 3651 (1993).
28. M. Ysobe and Y. Ueda, J. Phys. Soc. Jpn. 65, 1178 (1996).
29. A. W. Sandvik and D. K. Campbell (unpublished).
30. A. W. Sandvik, in Numerical Methods for Lattice Quantum Many-Body Problems, edited by D. J. Scalapino (Addison-Wesley, Redwood City, CA, in press).
31. A. W. Sandvik, A. V. Chubukov, and S. Sachdev, Phys. Rev. B 51, 16 483 (1995).
32. A. W. Sandvik and D. J. Scalapino, 53, R526 (1996).
33. A. W. Sandvik, Phys. Rev. B 52, R9831 (1995).
34. O. A. Starykh, A. W. Sandvik, and R. R. P. Singh, Phys. Rev. B 55, 14 953 (1997).
35. A. W. Sandvik, D. J. Scalapino, and P. Henelius, Phys. Rev. B 50, 10 474 (1994).
36. A. W. Sandvik and A. Sudbø, Europhys. Lett. 36, 443 (1996).
37. Phys. Rev. B 54, R3746 (1996).
38. E. Y. Loh, Jr. et al., Phys. Rev. B 41, 9301 (1990).
39. S. Miyashita, M. Takasu, and M. Suzuki, in Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems (Ref. 4), p. 114.
40. It has recently been noted that as (Formula presented) results in the zero winding number sector become exact even for a finite system;P. Henelius et. al (unpublished).
41. S. Eggert, I. Affleck, and M. Takahashi, Phys. Rev. Lett. 73, 332 (1994).
42. J. Boucher and L. P. Regnault, J. Phys. I6, 1939 (1996).
43. P. H. M. van Loosdrecht et al., Phys. Rev. Lett. 78, 487 (1997).
44. Y. Fuji et al., J. Phys. Soc. Jpn. 66, 326 (1997).
45. M. Weiden et al., Z. Phys. B 103, 1 (1997).
46. J. Riera and A. Dobry, Phys. Rev. B 51, 16098 (1995).
47. G. Castilla, S. Chakravarty, and V. J. Emery, Phys. Rev. Lett. 75, 1823 (1995).
48. D. Augier, D. Poilblanc, S. Haas, A. Delia, and E. Dagotto, Phys. Rev. B56, 5732 (1997).
49. K. Fabricius, A. Klümber, U. Löv, B. Büchner, and T. Lorenz, cond-mat/9705036 (unpublished).
50. J. E. Hirsch and E. Fradkin, Phys. Rev. 27, 4302 (1983).
51. E. Fradkin and J. E. Hirsch, Phys. Rev. B 27, 1680 (1983).
52. D. Augier and D. Poilblanc, cond-mat/9705032 (unpublished).
53. M. C. Cross and D. S. Fisher, Phys. Rev. B 19, 402 (1979).
54. D. C. Johnston, Phys. Rev. B 54, 13009 (1996).
55. S. Eggert, Phys. Rev. B 53, 5116 (1996).
56. P. C. Hohenberg and W. F. Brinkman, Phys. Rev. B 10, 128 (1974).
57. M. Greven, R. J. Birgeneau, and U. J. Wiese, Phys. Rev. Lett. 77, 1865 (1996).
58. B. Frischmuth, B. Ammon, and M. Troyer, Phys. Rev. B 54, R3714 (1996).
59. M. Troyer, M. E. Zhitomirsky, and K. Ueda, 55, R6117 (1997).
60. N. Kawashima, J. E. Gubernatis, and H. G. Evertz, Phys. Rev. B 50, 136 (1994).
61. N. Kawashima, J. Stat. Phys. 82, 131 (1996).
62. A. W. Sandvik, Phys. Rev. B56, 11 678 (1997).