Explicit gauge fixing for degenerate multiplets: A generic setup for topological orders

Journal of the Physical Society of Japan

Volumn 73, Issue 10, 2004, Pages 2604-2607

  Hatsugai, Yasuhiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Chern numbers; Degeneracy; Topological orders

Indexed keywords

ANISOTROPY; ARTICLE; CALCULATION; CHIRALITY; CONDUCTANCE; FERMION; MATERIALS HANDLING; POLARIZATION; QUANTUM CHEMISTRY; SUPERCONDUCTOR;

EID: 20444366206     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.73.2604     Document Type: Article

References (49)

1. Geometric Phases in Physics, ed. A. Shapere and F. Wilczek (World Scientific, Singapore, 1989).
2. X. G. Wen: Phys. Rev. B 40 (1989) 7387.
3. K. V. Klitzing, G. Dorda and M. Pepper: Phys. Rev. Lett. 45 (1980) 494.
4. T. Ando: J. Phys. Soc. Jpn. 37 (1974) 622.
5. H. Aoki and T. Ando: Solid State Commun. 38 (1981) 1079.
6. R. B. Laughlin: Phys. Rev. B 23 (1981) 5632.
7. D. J. Thouless, M. Kohmoto, P. Nightingale and M. den Nijs: Phys. Rev. Lett. 49 (1982) 405.
8. M. Kohmoto: Ann. Phys. (N.Y.) 160 (1985) 355.
9. R. B. Laughlin: Phys. Rev. Lett. 50 (1983) 1395.
10. Q. Niu, D. J. Thouless and Y. Wu: Phys. Rev. B 31 (1985) 3372.
11. S. Girvin, A. H. MacDonald and P. M. Platzman: Phys. Rev. Lett. 54 (1985) 581.
12. P. Strêda: J. Phys. C 15 (1982) L717.
13. F. D. M. Haldane: Phys. Rev. Lett. 50 (1983) 1153.
14. W. P. Su, J. R. Schrieffer and A. J. Heeger: Phys. Rev. Lett. 42 (1979) 1698.
15. T. Senthil, J. B. Marston and M. Fisher: Phys. Rev. B 60 (1999) 4245.
16. Y. Morita and Y. Hatsugai: Phys. Rev. B 62 (2000) 99.
17. Y. Hatsugai and S. Ryu: Phys. Rev. B 65 (2002) 212510.
18. G. E. Volovik: JETP Lett. 66 (1997) 493.
19. 3He (World Scientific, Singapore, 1992).
20. N. Read and D. Green: Phys. Rev. B 61 (2000) 10267.
21. Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa and Y. Tokura: Science 291 (2001) 2573.
22. D. J. Thouless: Phys. Rev. B 27 (1983) 6083.
23. S. Murakami, N. Nagaosa and S.-C. Zhang: Science 5 (2003) 1348.
24. R. D. King-Smith and D. Vanderblit: Phys. Rev. B 47 (1993) 1651.
25. S. Ryu and Y. Hatsugai: Phys. Rev. Lett. 89 (2002) 077002.
26. X. G. Wen, F. Wilczek and A. Zee: Phys. Rev. B 39 (1989) 11413.
27. I. Affleck and J. B. Marston: Phys. Rev. B 37 (1988) 3774.
28. J. Jain: Phys. Rev. Lett. 63 (1989) 199.
29. B. I. Halperin: Phys. Rev. B 25 (1982) 2185.
30. Y. Hatsugai: Phys. Rev. B 48 (1993) 11851.
31. T. Kennedy: J. Phys.: Condens. Matter 2 (1990) 5737.
32. P. Dirac: Lectures on Quantum Mechanics (Dover, New York, 1964).
33. M. V. Berry: Proc. R. Soc. London, Ser. A 392 (1984) 45.
34. F. Wilczek and A. Zee: Phys. Rev. Lett. 52 (1984) 2111.
35. T. Eguchi, P. B. Gilkey and A. J. Hanson: Phys. Rep. 66 (1980) 213.
36. B. Zumino: Current Algebra and Anomaly (World Scientific, Singapore, 1991) p. 362.
37. Y. Hatsugai: Phys. Rev. Lett. 71 (1993) 3697.
38. Y. Hatsugai: J. Phys.: Condens. Matter 9 (1997) 2507.
39. M. Sigrist and K. Ueda: Rev. Mod. Phys. 63 (1991) 239.
40. F. D. M. Haldane and E. H. Rezayi: Phys. Rev. B 31 (1985) 2529.
41. We require dim V = d ≥ 2 for the following discussions. However, one can freely supplement additional parameters. Then the case dim V = 1 is also within the analysis.
42. Y. Hatsugai, S. Ryu and M. Kohmoto: Phys. Rev. B 70 (2004) 054502.
43. B. I. Halperin: Proc. 18th Conf. Low Temperature Physics, 1987, Kyoto, Jpn. J. Appl. Phys. 26 (1987) Suppl. 26-3, p. 1913.
44. M. Kohmoto, B. I. Halperin and Y. S. Wu: Phys. Rev. B 45 (1992) 13488.
45. 1 which appears as a two-dimensional Brillouin zone or a couple of fluxes in the multiflux AB effect.
46. Φ. We use d′ to indicate it.
47. T. Kato: Prog. Theor. Phys. 4 (1949) 514.
48. J. E. Avron, R. Seiler and B. Simon: Phys. Rev. Lett. 51 (1983) 51.
49. J. E. Avron and R. Seiler: Phys. Rev. Lett. 54 (1985) 259.