Density of states for the π-flux state with bipartite real random hopping only: A weak disorder approach

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 6, 2003, Pages 642021-6420228

  Mudry, C ^a,b   Ryu, S ^c   Furusaki, A ^b  

^a PAUL SCHERRER INSTITUTE   (Switzerland)

^b KYOTO UNIVERSITY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CHIRALITY; DENSITY; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PREDICTION; THEORY;

EID: 0037301760     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (86)

1. J. T. Edwards and D. J. Thouless, J. Phys. C 4, 453 (1971).
2. F. Wegner, Z. Phys. B: Condens. Matter 44, 9 (1981).
3. C. Pryor and A. Zee, Phys. Rev. B 46, 3116 (1992).
4. I. A. Gruzberg, P. J. Hirschfeld, and A. V. Shytov, Phys. Rev. Lett. 87, 239703 (2001).
5. F. J. Dyson, Phys. Rev. 92, 1331 (1953).
6. G. Theodorou and M. H. Cohen, Phys. Rev. B 13, 4597 (1976).
7. T. P. Eggarter and R. Riedinger, Phys. Rev. B 18, 569 (1978).
8. R. Gade, Nucl. Phys. B 398, 499 (1993); R. Gade and F. Wegner, ibid. 360, 213 (1991); F. J. Wegner, Phys. Rev. B 19, 783 (1979).
9. R. Gade, Nucl. Phys. B 398, 499 (1993); R. Gade and F. Wegner, ibid. 360, 213 (1991); F. J. Wegner, Phys. Rev. B 19, 783 (1979).
10. R. Gade, Nucl. Phys. B 398, 499 (1993); R. Gade and F. Wegner, ibid. 360, 213 (1991); F. J. Wegner, Phys. Rev. B 19, 783 (1979).
11. A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).
12. A. A. Nersesyan, A. M. Tsvelik, and F. Wenger, Phys. Rev. Lett. 72, 2628 (1994); Nucl. Phys. B 438, 561 (1995).
13. A. A. Nersesyan, A. M. Tsvelik, and F. Wenger, Phys. Rev. Lett. 72, 2628 (1994); Nucl. Phys. B 438, 561 (1995).
14. T. Senthil and M. P. A. Fisher, Phys. Rev. B 61, 9690 (2000).
15. M. Bocquet, D. Serban, and M. R. Zimbauer, Nucl. Phys. B 578, 628 (2000).
16. P. W. Brouwer, A. Furusaki, I. A. Gruzberg, and C. Mudry, Phys. Rev. Lett. 85, 1064 (2000).
17. A. Altland and M. Zirnbauer, Phys. Rev. B 55, 1142 (1997).
18. D. A. Ivanov, J. Math. Phys. 43, 126 (2002), and references therein.
19. R. Bundschuh, C. Cassanello, D. Serban, and M. R. Zirnbauer, Nucl. Phys. B 532, 689 (1998); Phys. Rev. B 59, 4382 (1999).
20. R. Bundschuh, C. Cassanello, D. Serban, and M. R. Zirnbauer, Nucl. Phys. B 532, 689 (1998); Phys. Rev. B 59, 4382 (1999).
21. A. Altland and R. Merkt, Nucl. Phys. B 607, 511 (2001).
22. O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B 63, 224204 (2001).
23. P. W. Brouwer, C. Mudry, B. D. Simons, and A. Altland, Phys. Rev. Lett. 81, 862 (1998).
24. P. W. Brouwer, C. Mudry, and A. Furusaki, Phys. Rev. Lett. 84, 2913 (2000); M. Titov, P. W. Brouwer, A. Furusaki, and C. Mudry, Phys. Rev. B 63, 235318 (2001).
25. P. W. Brouwer, C. Mudry, and A. Furusaki, Phys. Rev. Lett. 84, 2913 (2000); M. Titov, P. W. Brouwer, A. Furusaki, and C. Mudry, Phys. Rev. B 63, 235318 (2001).
26. D. G. Shelton and A. M. Tsvelik, Phys. Rev. B 57, 14 242 (1998).
27. M. B. Hastings and S. L. Sondhi, Phys. Rev. B 64, 094204 (2001).
28. A. Comtet, J. Desbois, and C. Monthus, Ann. Phys. (N.Y.) 239, 312 (1995).
29. L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12 970 (1997).
30. H. Mathur, Phys. Rev. B 56, 15 794 (1997).
31. T. Fukui, Nucl. Phys. B 562, 477 (1999).
32. S. Guruswamy, A. LeClair, and A. W. W. Ludwig, Nucl. Phys. B 583, 475 (2000).
33. A. Altland and B. D. Simons, Nucl. Phys. B 562, 445 (1999).
34. M. Fabrizio and C. Castellani, Nucl. Phys. B 583, 542 (2000).
35. O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B 65, 064206 (2002).
36. C. Dasgupta and S. K. Ma, Phys. Rev. B 22, 1305 (1980).
37. Y. Hatsugai, X.-G. Wen, and M. Kohmoto, Phys. Rev. B 56, 1061 (1997).
38. Y. Morita and Y. Hatsugai, Phys. Rev. Lett. 79, 3728 (1997); Phys. Rev. B 58, 6680 (1998).
39. Y. Morita and Y. Hatsugai, Phys. Rev. Lett. 79, 3728 (1997); Phys. Rev. B 58, 6680 (1998).
40. S. Ryu and Y. Hatsugai, Phys. Rev. B 65, 033301 (2002).
41. D. Carpentier and P. Le Doussal, Nucl. Phys. B 588, 565 (2000).
42. C. de C. Chamon, C. Mudry, and X.-G. Wen, Phys. Rev. B 53, R7638 (1996).
43. C. Mudry, C. Chamon, and X.-G. Wen, Nucl. Phys. B. 466, 383 (1996).
44. C. C. Chamon, C. Mudry, and X.-G. Wen, Phys. Rev. Lett. 77, 4194 (1996).
45. I. I. Kogan, C. Mudry, and A. M. Tsvelik, Phys. Rev. Lett. 77, 707 (1996).
46. H. E. Castillo, C. de C. Chamon, E. Fradkin, P. M. Goldbart, and C. Mudry, Phys. Rev. B 56, 10 668 (1997).
47. C. Mudry and X.-G. Wen, Nucl. Phys. B 549, 613 (1999).
48. B. Horovitz and P. Le Doussal, Phys. Rev. B 65, 125323 (2002).
49. D. Bernard, Nucl. Phys. B 441, 471 (1995); D. Bernard, in Low-Dimensional Applications of Quantum Field Theory, edited by L. Baulieu, V. Kazakov, M. Picco, and P. Windey, Vol. 362 of NATO Advanced Study Institute, Series B: Physics (Plenum Press, New York, 1997); D. Bernard, hep-th/9509137 (unpublished).
50. D. Bernard, Nucl. Phys. B 441, 471 (1995); D. Bernard, in Low-Dimensional Applications of Quantum Field Theory, edited by L. Baulieu, V. Kazakov, M. Picco, and P. Windey, Vol. 362 of NATO Advanced Study Institute, Series B: Physics (Plenum Press, New York, 1997); D. Bernard, hep-th/9509137 (unpublished).
51. D. Bernard, Nucl. Phys. B 441, 471 (1995); D. Bernard, in Low-Dimensional Applications of Quantum Field Theory, edited by L. Baulieu, V. Kazakov, M. Picco, and P. Windey, Vol. 362 of NATO Advanced Study Institute, Series B: Physics (Plenum Press, New York, 1997); D. Bernard, hep-th/9509137 (unpublished).
52. D. Carpentier and P. Le Doussal, Phys. Rev. E 63, 026110 (2001).
53. B. Derrida and H. Spohn, J. Stat. Phys. 51, 817 (1988).
54. E. Buffet, A. Patrick, and J. V. Pulé, J. Phys. A 26, 1823 (1993).
55. M. P. A. Fisher and E. Fradkin, Nucl. Phys. B 251, 457 (1985); E. Fradkin, Phys. Rev. B 33, 3257 (1986); 33, 3263 (1986).
56. M. P. A. Fisher and E. Fradkin, Nucl. Phys. B 251, 457 (1985); E. Fradkin, Phys. Rev. B 33, 3257 (1986); 33, 3263 (1986).
57. M. P. A. Fisher and E. Fradkin, Nucl. Phys. B 251, 457 (1985); E. Fradkin, Phys. Rev. B 33, 3257 (1986); 33, 3263 (1986).
58. HWK can be interpreted as the Hamiltonian for a single flavor of Dirac fermion subjected to random scalar, vector, and mass potentials studied in Refs. 9 and 43.
59. The Hermitian energy perturbation in Eq. (5.7) of Ref. 27 differs from the non-Hermitian energy perturbation in Eq. (3.13c). Our choice has the advantage that the RG equations obeyed by the DOS has the same structure as had we chosen to work with the representation defined by Eq. (3.11).
60. 2 in the zero mode of HMDH were inadvertently exchanged in Ref. 32.
61. A. Kolmogorov, I. Petrovsky, and N. Piscounov, Moscow Univ. Math. Bull. (Engl. Transl.) 1, 1 (1937).
62. M. Bramson, Convergence of Solutions of the Kolmogorov Equation to Traveling Waves, Memoirs of the American Mathematical Society, No. 285 (American Mathematical Society, Providence, RI, 1983).
63. a′ at infinity. The boundary conditions are uniquely fixed by the phase of the complex parameter u. The choice u/|u| = -i imposes the boundary condition that the bosonized fields vanish at infinity. We are indebted to A. W. W. Ludwig for clarification of this point.
64. D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B 271, 93 (1986).
65. M. R. Gaberdiel and H. G. Kausch, Phys. Lett. B 386, 131 (1996).
66. See also H. G. Kausch, hep-th/9510149 (unpublished).
67. L. Rozansky and H, Saleur, Nucl. Phys. B 376, 461 (1992).
68. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, JETP Lett. 43, 440 (1986); Sov. Phys. JETP 64, 1352 (1986); Phys. Lett. A 134, 488 (1989).
69. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, JETP Lett. 43, 440 (1986); Sov. Phys. JETP 64, 1352 (1986); Phys. Lett. A 134, 488 (1989).
70. B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, JETP Lett. 43, 440 (1986); Sov. Phys. JETP 64, 1352 (1986); Phys. Lett. A 134, 488 (1989).
71. O. N. Dorokhov, JETP Lett. 36, 318 (1982); P. A. Mello, P. Pereyra, and N. Kumar, Ann. Phys. (N.Y.) 181, 290 (1988).
72. O. N. Dorokhov, JETP Lett. 36, 318 (1982); P. A. Mello, P. Pereyra, and N. Kumar, Ann. Phys. (N.Y.) 181, 290 (1988).
73. For a review see C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
74. F. Wegner, Z. Phys. B: Condens. Matter 36, 209 (1980); in Localization and Metal Insulator Transitions, edited by H. Fritzsche and D. Adler, Institute for Amorphous Studies Series (Plenum Press, New York, 1985).
75. F. Wegner, Z. Phys. B: Condens. Matter 36, 209 (1980); in Localization and Metal Insulator Transitions, edited by H. Fritzsche and D. Adler, Institute for Amorphous Studies Series (Plenum Press, New York, 1985).
76. V. I. Fal'ko and K. B. Efetov, Europhys. Lett. 32, 627 (1995); Phys. Rev. B 52, 17413 (1996).
77. V. I. Fal'ko and K. B. Efetov, Europhys. Lett. 32, 627 (1995); Phys. Rev. B 52, 17413 (1996).
78. J.-S. Caux, Phys. Rev. Lett. 81, 4196 (1998).
79. A. Dohmen, P. Freche, and M. Janssen, Phys. Rev. Lett. 76, 4207 (1996).
80. B. Huckestein and R. Klesse, Phys. Rev. B 55, R7303 (1997).
81. A. D. Mirlin, Phys. Rep. 326, 259 (2000); A. D. Mirlin and F. Evers, Phys. Rev. B 62, 7920 (2000); F. Evers, A. Mildenberger, and A. D. Mirlin, ibid. 64, 241303(R) (2001).
82. A. D. Mirlin, Phys. Rep. 326, 259 (2000); A. D. Mirlin and F. Evers, Phys. Rev. B 62, 7920 (2000); F. Evers, A. Mildenberger, and A. D. Mirlin, ibid. 64, 241303(R) (2001).
83. A. D. Mirlin, Phys. Rep. 326, 259 (2000); A. D. Mirlin and F. Evers, Phys. Rev. B 62, 7920 (2000); F. Evers, A. Mildenberger, and A. D. Mirlin, ibid. 64, 241303(R) (2001).
84. F. Wegner, Z. Phys. B: Condens. Matter 51, 279 (1983).
85. M. R. Zirnbauer, hep-th/9905054 (unpublished).
86. M. J. Bhaseen, I. I. Kogan, O. A. Soloviev, N. Taniguchi, and A. M. Tsvelik, Nucl. Phys. B 580, 688 (2000).