Symmetries of multifractal spectra and field theories of anderson localization

Physical Review Letters

Volumn 107, Issue 8, 2011, Pages

  Gruzberg, I A ^a   Ludwig, A W W ^b   Mirlin, A D ^c,d   Zirnbauer, M R ^e  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^d PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

^e UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON LOCALIZATION; ANDERSON TRANSITION; CONFORMAL INVARIANCE; CORRELATION FUNCTION; CRITICAL POINTS; DISORDERED SYSTEM; FIELD THEORY; LOCAL DENSITY OF STATE; MULTIFRACTAL SPECTRUM; SYMMETRY RELATIONS; TARGET SPACE; WEYL GROUP;

PROBABILITY DISTRIBUTIONS;

FRACTALS;

EID: 80051922291     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.107.086403     Document Type: Article

References (62)

1. 50 years of Anderson Localization, edited by, E. Abrahams, (World Scientific, Singapore, 2010).
2. For a review, see F. Evers and A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.1355
3. D.S. Wiersma, Nature (London) 390, 671 (1997). NATUAS 0028-0836 10.1038/37757 (Pubitemid 28016351)
4. J. Billy, Nature (London) 453, 891 (2008); NATUAS 0028-0836 10.1038/nature07000 (Pubitemid 351832566)
5. G. Roati, Nature (London) 453, 895 (2008). NATUAS 0028-0836 10.1038/nature07071 (Pubitemid 351832573)
6. S. Faez, Phys. Rev. Lett. 103, 155703 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.155703
7. G. Lemarié, Phys. Rev. Lett. 105, 090601 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.090601
8. A. Altland and M.R. Zirnbauer, Phys. Rev. B PRBMDO 0163-1829 55, 1142 (1997). 10.1103/PhysRevB.55.1142
9. M.R. Zirnbauer, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 37, 4986 (1996). 10.1063/1.531675
10. P. Heinzner, A. Huckleberry, and M.R. Zirnbauer, Commun. Math. Phys. 257, 725 (2005). CMPHAY 0010-3616 10.1007/s00220-005-1330-9 (Pubitemid 40906204)
11. A. Richardella, Science 327, 665 (2010). SCIEAS 0036-8075 10.1126/science.1183640
12. A.D. Mirlin, Phys. Rev. Lett. 97, 046803 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.046803 (Pubitemid 44147307)
13. A.D. Mirlin and Y.V. Fyodorov, Phys. Rev. Lett. 72, 526 (1994); PRLTAO 0031-9007 10.1103/PhysRevLett.72.526
14. A.D. Mirlin Y.V. Fyodorov J. Phys. I (France) JPGCE8 1155-4304 4, 655 (1994). 10.1051/jp1:1994168
15. Y.V. Fyodorov and D.V. Savin, JETP Lett. 80, 725 (2004); JTPLA2 0021-3640 10.1134/1.1868794 (Pubitemid 40272653)
16. D.V. Savin, Y.V. Fyodorov, and H.-J. Sommers, JETP Lett. 82, 544 (2005); JTPLA2 0021-3640 10.1134/1.2150877 (Pubitemid 43006832)
17. Y.V. Fyodorov, D.V. Savin, and H.-J. Sommers, J. Phys. A JPHAC5 0305-4470 38, 10731 (2005). 10.1088/0305-4470/38/49/017 (Pubitemid 41706115)
18. Recent work, C. Monthus, B. Berche, and C. Chatelain, J. Stat. Mech. 1742-5468 (2009) P12002, emphasized an analogy between Eq. and the Gallavotti-Cohen symmetry relation, 10.1088/1742-5468/2009/12/P12002
19. G. Gallavotti and E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995), from nonequilibrium statistical physics. PRLTAO 0031-9007 10.1103/PhysRevLett.74.2694
20. H. Obuse, Phys. Rev. B PRBMDO 1098-0121 82, 035309 (2010). 10.1103/PhysRevB.82.035309
21. B. Duplantier and A.W.W. Ludwig, Phys. Rev. Lett. 66, 247 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.66.247
22. A.M. Polyakov, Sov. Phys. JETP SPHJAR 0038-5646 39, 10 (1974)
23. [A.M. Polyakov Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 66, 23 (1974)];
24. M.E. Fisher, in Proceedings of the Nobel Symposium 24, edited by, B. Lundqvist, and, S. Lundqvist, (Academic, London, 1973), p. 16;
25. see also P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer, New York, 1997).
26. Nonderivative operators, that is, operators which are not derivatives of other operators, are conventionally called quasiprimary operators [A.A. Belavin, A.M. Polyakov, and A.B. Zamolodchikov, Nucl. Phys. NUPBBO 0550-3213 B241, 333 (1984)] in the context of conformal symmetry. 10.1016/0550-3213(84)90052-X
27. q are quasiprimary;
28. see also H. Obuse, A.R. Subramaniam, A. Furusaki, I.A. Gruzberg, A.W.W. Ludwig, Phys. Rev. Lett. PRLTAO 0031-9007 98, 156802 (2007); 10.1103/PhysRevLett.98.156802 (Pubitemid 46582695)
29. H. Obuse A.R. Subramaniam A. Furusaki I.A. Gruzberg A.W.W. Ludwig Physica (Amsterdam) PELNFM 1386-9477 40E, 1404 (2008). 10.1016/j.physe.2007.09.024 (Pubitemid 351289225)
30. K.B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, England, 1987);
31. A.D. Mirlin, Phys. Rep. 326, 259 (2000); PRPLCM 0370-1573 10.1016/S0370-1573(99)00091-5
32. M.R. Zirnbauer, arXiv:math-ph/0404058.
33. A.D. Mirlin, A. Müller-Groeling, and M.R. Zirnbauer, Ann. Phys. (N.Y.) 236, 325 (1994). APNYA6 0003-4916 10.1006/aphy.1994.1115
34. A. Alldridge, arXiv:1004.0732. This paper exploits the Iwasawa decomposition of totally noncompact superspaces. On the other hand, the σ models we deal with have compact fermion-fermion sectors, so that, strictly speaking, the Iwasawa decomposition does not exist. However, it is possible to overcome this technical difficulty and derive an appropriate generalization of the integral formula and the Weyl symmetry theorem for all symmetry classes except for the chiral ones
35. [M.R. Zirnbauer (to be published)].
36. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic, New York, 1978).
37. S. Helgason, Groups and Geometric Analysis (Academic, New York, 1984).
38. H. Obuse, Phys. Rev. Lett. 98, 156802 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.156802 (Pubitemid 46582695)
39. A. Mildenberger and F. Evers, Phys. Rev. B PRBMDO 1098-0121 75, 041303 (2007); 10.1103/PhysRevB.75.041303
40. H. Obuse, Phys. Rev. B PRBMDO 1098-0121 78, 115301 (2008). 10.1103/PhysRevB.78.115301
41. H. Obuse, Phys. Rev. Lett. 101, 116802 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.101.116802
42. F. Evers, A. Mildenberger, and A.D. Mirlin, Phys. Rev. Lett. 101, 116803 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.116803
43. A. Rodriguez, L.J. Vasquez, and R.A. Römer, Phys. Rev. B PRBMDO 1098-0121 78, 195107 (2008). 10.1103/PhysRevB.78.195107
44. I.A. Gruzberg, A.W.W. Ludwig, and N. Read, Phys. Rev. Lett. 82, 4524 (1999); PRLTAO 0031-9007 10.1103/PhysRevLett.82.4524
45. E.J. Beamond, J. Cardy, and J.T. Chalker, Phys. Rev. B PRBMDO 0163-1829 65, 214301 (2002). 10.1103/PhysRevB.65.214301
46. A.D. Mirlin, F. Evers, and A. Mildenberger, J. Phys. A JPHAC5 0305-4470 36, 3255 (2003). 10.1088/0305-4470/36/12/323
47. A.R. Subramaniam, I.A. Gruzberg, and A.W.W. Ludwig, Phys. Rev. B PRBMDO 1098-0121 78, 245105 (2008). 10.1103/PhysRevB.78.245105
48. A.R. Subramaniam, Phys. Rev. Lett. 96, 126802 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.126802
49. A.M. Tsvelik, Phys. Rev. B PRBMDO 0163-1829 51, 9449 (1995); 10.1103/PhysRevB.51.9449
50. M.J. Bhaseen, Nucl. Phys. NUPBBO 0550-3213 B618, 465 (2001); 10.1016/S0550-3213(01)00432-1 (Pubitemid 33378290)
51. A.W.W. Ludwig, arXiv:cond-mat/0012189.
52. A.P. Schnyder, Phys. Rev. B PRBMDO 1098-0121 78, 195125 (2008); 10.1103/PhysRevB.78.195125
53. A.P. Schnyder, S. Ryu, and A.W.W. Ludwig, Phys. Rev. Lett. 102, 196804 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.196804
54. C. Mudry, C. Chamon, and X.-G. Wen, Nucl. Phys. NUPBBO 0550-3213 B466, 383 (1996); 10.1016/0550-3213(96)00128-9 (Pubitemid 126165309)
55. J.-S. Caux, Phys. Rev. Lett. 81, 4196 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.81.4196
56. C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997). RMPHAT 0034-6861 10.1103/RevModPhys.69.731 (Pubitemid 127098258)
57. P.W. Brouwer, Phys. Rev. Lett. 85, 1064 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.1064
58. A.W.W. Ludwig, Phys. Rev. B PRBMDO 0163-1829 50, 7526 (1994). 10.1103/PhysRevB.50.7526
59. F. Merz and J.T. Chalker, Phys. Rev. B PRBMDO 0163-1829 66, 054413 (2002). 10.1103/PhysRevB.66.054413
60. B. Duplantier, Phys. Rev. Lett. 84, 1363 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.1363
61. I. Rushkin, J. Phys. A 1751-8113 40, 2165 (2007); 10.1088/1751-8113/40/9/ 020
62. A. Belikov, I.A. Gruzberg, and I. Rushkin, J. Phys. A 1751-8113 41, 285006 (2008). 10.1088/1751-8113/41/28/285006