Self-consistent fluctuation theory for strongly correlated electron systems

Journal of the Physical Society of Japan

Volumn 79, Issue 9, 2010, Pages

  Kusunose, Hiroaki ^a  

^a EHIME UNIVERSITY   (Japan)

Author keywords

Hubbard model; Impurity Anderson model; Mermin Wagner theorem; Parquet equation; Quantum critical point; Self consistent renormalization theory; Two particle self consistency

Indexed keywords

EID: 77957080345     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJ.79.094707     Document Type: Article

References (56)

1. N. F. Mott: Proc. Phys. Soc., Sect. A 62 (1949) 416.
2. N. F. Mott: Metal Insulator Transitions (Taylor and Francis, London, 1990).
3. M. Imada, A. Fujimori, and Y. Tokura: Rev. Mod. Phys. 70 (1998) 1039.
4. C. Castellani, C. Di Castro, D. Feinberg, and J. Ranninger: Phys. Rev. Lett. 43 (1979) 1957.
5. G. Kotliar, E. Lange, and M. J. Rozenberg: Phys. Rev. Lett. 84 (2000) 5180.
6. P. Limelette, A. Georges, D. Jérome, P. Wzietek, P. Metcalf, and J. M. Honig: Science 302 (2003) 89.
7. Frontiers of Novel Superconductivity in Heavy Fermion Compounds, ed. Y. Ōnuki and Y. Kitaoka, J. Phys. Soc. Jpn. 76 (2007) No. 5, Special Topics.
8. T. Moriya and K. Ueda: Adv. Phys. 49 (2000) 555.
9. Y. Yanase, T. Jujo, T. Nomura, H. Ikeda, T. Hotta, and K. Yamada: Phys. Rep. 387 (2003) 1.
10. D. Manske: Theory of Unconventional Superconductors (Springer, Heidelberg, 2004).
11. N. E. Bickers, D. J. Scalapino, and S. R. White: Phys. Rev. Lett. 62 (1989) 961.
12. N. E. Bickers and D. J. Scalapino: Ann. Phys. (N. Y.) 193 (1989) 206.
13. N. E. Bickers and S. R. White: Phys. Rev. B 43 (1991) 8044.
14. G. Baym and L. P. Kadanoff: Phys. Rev. 124 (1961) 287.
15. G. Baym: Phys. Rev. 127 (1962) 1391.
16. 15) aim to give a prescription for the two-particle quantities to be conserving, however, most of recent studies using the FLEX served the conserving self-energy, and discussed mainly for superconducting transitions.
17. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg: Rev. Mod. Phys. 68 (1996) 13.
18. A. Georges: cond-mat/0403123.
19. T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler: Rev. Mod. Phys. 77 (2005) 1027.
20. N. D. Mermin and H. Wagner: Phys. Rev. Lett. 17 (1966) 1133
21. [Errata; 17 (1966) 1307].
22. The staggered magnetic susceptibility of the FLEX in the expression of the self-energy in the Hubbard model on a square lattice does not show a divergence except at T = 0. However, this Mermin-Wagner theorem is fulfilled in unphysical way, where the one-particle selfenergy is the origin of the suppression of the susceptibility instead of the vertex corrections.
23. The DMFT and its cluster extensions properly consider vertex corrections in frequency domain, but they neglect or treat insufficiently in the momentum domain.
24. The phenomenological correction in the dynamical vertex approximation remedies the violation of the Mermin-Wagner theorem, see A. A. Katanin, A. Toschi, and H. Held: Phys. Rev. B 80 (2009) 075104.
25. R. Shankar: Rev. Mod. Phys. 66 (1994) 129.
26. W. Metzner, C. Castellani, and C. Di Castro: Adv. Phys. 47 (1998) 317.
27. G. Y. Chitov and D. Sénéchal: Phys. Rev. B 52 (1995) 13487.
28. G. Y. Chitov and D. Sénéchal: Phys. Rev. B 57 (1998) 1444.
29. T. Moriya: Spin Fluctuations in Itinerant Electron Magnetism (Springer, Heidelberg, 1985).
30. T. Moriya and T. Takimoto: J. Phys. Soc. Jpn. 64 (1995) 960.
31. A. Kawabata: J. Phys. F 4 (1974) 1477.
32. J. A. Hertz: Phys. Rev. B 14 (1976) 1165.
33. A. J. Millis: Phys. Rev. B 48 (1993) 7183.
34. Y. M. Vilk and A.-M. S. Tremblay: J. Phys. I 7 (1997) 1309.
35. For example, see, Theoretical Methods for Strongly Correlated Electrons, ed. D. Sénéchal, A.-M. S. Tremblay, and C. Bourbonnais (Springer, New York, 2004) Sects. 6 and 8.
36. C. de Dominicis and P. C. Martin: J. Math. Phys. 5 (1964) 14;
37. C. de Dominicis and P. C. Martin: J. Math. Phys. 5 (1964) 31.
38. C.-X. Chen and N. E. Bickers: Solid State Commun. 82 (1992) 311.
39. Exactly speaking, the two-particle conservation law requires the Aslamasov-Larkin process with two collective fluctuation exchanges in the particle-hole irreducible vertex, which is not included in the parquet formalism.
40. V. Janiš and P. Augustinský: Phys. Rev. B 75 (2007) 165108.
41. V. Janiš and P. Augustinský: Phys. Rev. B 77 (2008) 085106.
42. V. Janis: cond-mat/9806118v1.
43. Y. Takada: Phys. Rev. B 52 (1995) 12708.
44. N. E. Bickers and D. J. Scalapino: Phys. Rev. B 46 (1992) 8050.
45. The attempts in this direction, see S. X. Yang, H. Fotso, J. Liu, T. A. Maier, K. Tomko, E. F. D'Azevedo, R. T. Scalettar, T. Pruschke, and M. Jarrell: arXiv:0906.4736v1.
46. A. M. Tsvelik and P. B. Wiegmann: Phys. Lett. A 89 (1982) 368.
47. A. C. Hewson: The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, U. K., 1993).
48. T. A. Costi, A. C. Hewson, and V. Zlatić: J. Phys.: Condens. Matter 6 (1994) 2519.
49. D. C. Langreth: Phys. Rev. 150 (1966) 516.
50. K. Yosida and K. Yamada: Prog. Theor. Phys. Suppl. 46 (1970) 244.
51. K. Yamada: Prog. Theor. Phys. 53 (1975) 970.
52. V. Zlatić, B. Horvatić, and D. Šokč ević: Z. Phys. B 59 (1985) 151.
53. B. Horvatić, D. Šokčević, and V. Zlatić: Phys. Rev. B 36 (1987) 675.
54. T. Moriya, Y. Takahashi, and K. Ueda: J. Phys. Soc. Jpn. 59 (1990) 2905.
55. H. Kusunose: J. Phys. Soc. Jpn. 75 (2006) 054713.
56. It has argued the practical algorithm for the vertex terms with a partial use of the FFT, see H. Ikeda, S. Shinkai, and K. Yamada: J. Phys. Soc. Jpn. 77 (2008) 064707.