Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances

Journal of the Physical Society of Japan

Volumn 74, Issue 6, 2005, Pages 1674-1677

  Fukui, Takahiro ^a   Hatsugai, Yasuhiro ^b   Suzuki, Hiroshi ^a  

^a IBARAKI UNIVERSITY   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Berry connection; Chern number; Lattice gauge theory; Quantum Hall effect

Indexed keywords

ANALYTIC METHOD; ARTICLE; CONDUCTANCE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; THEORETICAL MODEL;

EID: 21644459893     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.74.1674     Document Type: Article

References (19)

1. X. G. Wen: Phys. Rev. B 40 (1989) 7387.
2. Y. Hatsugai: J. Phys. Soc. Jpn. 73 (2004) 2604.
3. Y. Hatsugai: J. Phys. Soc. Jpn. 74 (2005) 1374.
4. D. J. Thouless, M. Kohmoto, P. Nightingale and M. den Nijs: Phys. Rev. Lett. 49 (1982) 405.
5. M. Kohmoto: Ann. Phys. 160 (1985) 355.
6. M. V. Berry: Proc. R. Soc. London, Ser. A 392 (1984) 45.
7. B. Simons: Phys. Rev. Lett. 51 (1983) 2167.
8. T. Senthil, J. B. Marston and M. P. A. Fisher: Phys. Rev. B 60 (1999) 4245.
9. Y. Morita and Y. Hatsugai: Phys. Rev. B 62 (2000) 99.
10. S. Murakami, N. Nagaosa and S.-C. Zhang: Science 5 (2003) 1348.
11. F. D. M. Haldane: Phys. Rev. Lett. 93 (2004) 206602.
12. M. Lüschen Commun. Math. Phys. 85 (1982) 39.
13. A. Phillips: Ann. Phys. 161 (1985) 399.
14. A. Phillips and D. Stone: Commun. Math. Phys. 103 (1986) 599.
15. A. Phillips and D. Stone: Commun. Math. Phys. 131 (1990) 255.
16. T. Fujiwara, H. Suzuki and K. Wu: Prog. Theor. Phys. 105 (2001) 789.
17. M. Lüscher: Nucl. Phys. B 549 (1999) 295, Sect. 7.
18. For higher dimensional lattices, this uniqueness of lattice Chern numbers holds if the admissibility is modified to F̃μν(kℓ) < ε with a certain constant ε ≤ π/3.
19. F. Wilczek and A. Zee: Phys. Rev. Lett. 52 (1984) 2111.