Γ(2) modular symmetry, renormalization group flow and the quantum hall effect

Journal of Physics A: Mathematical and General

Volumn 33, Issue 1, 2000, Pages 39-55

  Georgelin, Yvon ^a   Masson, Thierry ^b   Wallet, Jean Christophe ^a  

^a Orsay Campus   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034645709     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/1/303     Document Type: Article

References (42)

1. Prange R E and Girvin S M (ed) 1990 The Quantum Hall Effect 2nd edn (New York: Springer) See also Sarma S D and Pinczuk A (ed) 1997 Perspectives in Quantum Hall Effect (New York: Wiley)
2. Prange R E and Girvin S M (ed) 1990 The Quantum Hall Effect 2nd edn (New York: Springer) See also Sarma S D and Pinczuk A (ed) 1997 Perspectives in Quantum Hall Effect (New York: Wiley)
3. von Klitzing K, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
4. Tsui D C, Störmer H L and Gossard AC 1982 Phys. Rev. Lett. 48 1559
5. Laughlin R B 1983 Phys. Rev. Lett. 50 1385 Haldane F D 1983 Phys. Rev. Lett. 51 605 Halperin B I 1984 Phys. Rev. Lett. 52 1583
6. Laughlin R B 1983 Phys. Rev. Lett. 50 1385 Haldane F D 1983 Phys. Rev. Lett. 51 605 Halperin B I 1984 Phys. Rev. Lett. 52 1583
7. Laughlin R B 1983 Phys. Rev. Lett. 50 1385 Haldane F D 1983 Phys. Rev. Lett. 51 605 Halperin B I 1984 Phys. Rev. Lett. 52 1583
8. Kivelson S, Lee D H and Zhang S C 1992 Phys. Rev. B 46 2223
9. Lütken C A and Ross G G 1992 Phys. Rev. B 45 11837 Lütken C A and Ross G G 1993 Phys. Rev. B 48 2500 Fradkin E and Kivelson S 1996 Nucl. Phys. B 474 543
10. Lütken C A and Ross G G 1992 Phys. Rev. B 45 11837 Lütken C A and Ross G G 1993 Phys. Rev. B 48 2500 Fradkin E and Kivelson S 1996 Nucl. Phys. B 474 543
11. Lütken C A and Ross G G 1992 Phys. Rev. B 45 11837 Lütken C A and Ross G G 1993 Phys. Rev. B 48 2500 Fradkin E and Kivelson S 1996 Nucl. Phys. B 474 543
12. Shapere A and Wilczek F 1989 Nucl. Phys. B 320 669
13. Lütken C A 1993 Nucl. Phys. B 396 670
14. Georgelin Y, Masson T and Wallet J C 1997 J. Phys. A: Math. Gen. 30 5065
15. Dolan B P 1999 Nucl. Phys. B 554 487 (Dolan B P 1998 Modular invariance universality and crossover in the QHE Preprint cond-mat/9809294) Dolan B P 1999 J. Phys. A: Math. Gen. 32 L243 (Dolan B P 1998 Duality and the modular group in QHE Preprint cond-mat/9805171)
16. Dolan B P 1999 Nucl. Phys. B 554 487 (Dolan B P 1998 Modular invariance universality and crossover in the QHE Preprint cond-mat/9809294) Dolan B P 1999 J. Phys. A: Math. Gen. 32 L243 (Dolan B P 1998 Duality and the modular group in QHE Preprint cond-mat/9805171)
17. Dolan B P 1999 Nucl. Phys. B 554 487 (Dolan B P 1998 Modular invariance universality and crossover in the QHE Preprint cond-mat/9809294) Dolan B P 1999 J. Phys. A: Math. Gen. 32 L243 (Dolan B P 1998 Duality and the modular group in QHE Preprint cond-mat/9805171)
18. Dolan B P 1999 Nucl. Phys. B 554 487 (Dolan B P 1998 Modular invariance universality and crossover in the QHE Preprint cond-mat/9809294) Dolan B P 1999 J. Phys. A: Math. Gen. 32 L243 (Dolan B P 1998 Duality and the modular group in QHE Preprint cond-mat/9805171)
19. Cardy J 1982 Nucl. Phys. B 203 17 Cardy J and Rabinovici E 1982 Nucl. Phys. B 203 1
20. Cardy J 1982 Nucl. Phys. B 203 17 Cardy J and Rabinovici E 1982 Nucl. Phys. B 203 1
21. Carpentier D 1999 J. Phys. A: Math. Gen. 32 3865 and references therein
22. Seiberg N and Witten E 1994 Nucl. Phys. B 426 19 Latorre J I and Lütken C A 1988 Phys. Lett. B 421 217 Ritz A 1998 Phys. Lett. B 434 54
23. Seiberg N and Witten E 1994 Nucl. Phys. B 426 19 Latorre J I and Lütken C A 1988 Phys. Lett. B 421 217 Ritz A 1998 Phys. Lett. B 434 54
24. Seiberg N and Witten E 1994 Nucl. Phys. B 426 19 Latorre J I and Lütken C A 1988 Phys. Lett. B 421 217 Ritz A 1998 Phys. Lett. B 434 54
25. Levy L P et al 1998 Magnetization oscillations at fractional filling factors Institute for Theoretical Physics Conf. on Disorder and Interactions in Quantum Hall and Mesoscopic Systems (Santa Barbara, CA, 1998)
26. Dykhne A M and Ruzin I M 1994 Phys. Rev. B 50 2369 Ruzin I M and Feng S 1995 Phys. Rev. Lett. 74 154
27. Dykhne A M and Ruzin I M 1994 Phys. Rev. B 50 2369 Ruzin I M and Feng S 1995 Phys. Rev. Lett. 74 154
28. Rankin RA 1977 Modular Forms and Functions (Cambridge: Cambridge University Press)
29. Georgelin Y and Wallet J C 1997 Phys. Lett. A 224 303
30. Jain J K 1997 Phys. Rev. B 41 7653
31. Hilke M et al 1998 Nature 395 675
32. Hilke M et al 1999 Europhys. Lett. 46 775 (Hilke M et al 1998 Semi circle: An exact relation in the integer or fractional quantum Hall effect Preprint cond-mat/9810217)
33. Hilke M et al 1999 Europhys. Lett. 46 775 (Hilke M et al 1998 Semi circle: An exact relation in the integer or fractional quantum Hall effect Preprint cond-mat/9810217)
34. Burgess C P and Lütken C A 1999 Phys. Lett. B 451 365 (Burgess C P and Lütken C A 1998 On the implication of discrete symmetries for the β-function of quantum Hall system Preprint cond-mat/9812396) Taniguchi N 1998 Nonperturbative renormalization group function for quantum Hall plateaus transitions imposed by global symmetries Preprint cond-mat/9810334
35. Burgess C P and Lütken C A 1999 Phys. Lett. B 451 365 (Burgess C P and Lütken C A 1998 On the implication of discrete symmetries for the β-function of quantum Hall system Preprint cond-mat/9812396) Taniguchi N 1998 Nonperturbative renormalization group function for quantum Hall plateaus transitions imposed by global symmetries Preprint cond-mat/9810334
36. Burgess C P and Lütken C A 1999 Phys. Lett. B 451 365 (Burgess C P and Lütken C A 1998 On the implication of discrete symmetries for the β-function of quantum Hall system Preprint cond-mat/9812396) Taniguchi N 1998 Nonperturbative renormalization group function for quantum Hall plateaus transitions imposed by global symmetries Preprint cond-mat/9810334
37. Pruisken A M M 1985 Phys. Rev. B 32 2636 Pruisken A M M 1987 Nucl. Phys. B 285 61
38. Pruisken A M M 1985 Phys. Rev. B 32 2636 Pruisken A M M 1987 Nucl. Phys. B 285 61
39. Khmel'niskii D E 1983 Pisma Zh. Eksp. Teor. Fiz. 38 454
40. For a general discussion see Huckestein B 1995 Rev. Mod. Phys. 67 357
41. Shahar D et al 1997 Phys. Rev. Lett. 79 479
42. Sondhi S L, Girvin S M, Carini J P and Shahar D 1997 Rev. Mod. Phys. 69 315