Extended dynamical mean-field theory and (formula presented) method

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 8, 2002, Pages 1-20

  Sun, Ping ^a   Kotliar, Gabriel ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85038967163     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.085120     Document Type: Article

References (64)

1. A. Georges, G. Kotliar, W. Krauth, andM.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
2. P.G.J. van Dongen, Phys. Rev. Lett. 67, 757 (1991);
3. P.G.J. van DongenPhys. Rev. B 49, 7904 (1993);
4. Phys. Rev. BP.G.J. van Dongen50, 14 016 (1994);
5. Phys. Rev. BP.G.J. van Dongen54, 1584 (1996).
6. A. Schiller and K. Ingersent, Phys. Rev. Lett. 75, 113 (1995);
7. G. Zaránd, D.L. Cox, andA. Schiller, Phys. Rev. B 62, R16 227 (2000).
8. M.H. Hettler, A.N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, andH.R. Krishnamurthy, Phys. Rev. B 58, R7475 (1998);
9. Phys. Rev. BM.H. Hettler, M. Mukherjee, M. Jarrell, andH.R. Krishnamurthy, 61, 12 739 (2000).
10. S. Biermann, A. Georges, A. Lichtenstein, andT. Giamarchi, Phys. Rev. Lett. 87, 276405 (2001).
11. G. Kotliar, S. Savrasov, G. Palsson, andG. Biroli, Phys. Rev. Lett. 87, 186401 (2001) and references therein.
12. G. Biroli and G. Kotliar, Phys. Rev. B 65, 155112 (2002).
13. S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993).
14. H. Kajueter, Ph.D. thesis, Rutgers University, 1996.
15. Q. Si, S. Rabello, K. Ingersent, andJ.L. Smith, Nature (London) 413, 804 (2001);
16. J.L. Smith and Q. Si, Phys. Rev. B 61, 5184 (2000);
17. Q. Si and J.L. Smith, Phys. Rev. Lett. 77, 3391 (1996).
18. O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999).
19. R. Chitra and G. Kotliar, Phys. Rev. Lett. 84, 3678 (2000);
20. R. Chitra G. KotliarPhys. Rev. B 63, 115110 (2001).
21. Y. Motome and G. Kotliar, Phys. Rev. B 62, 12 800 (2000).
22. S. Pankov, G. Kotliar, andY. Motome, Phys. Rev. B 66, 045117 (2002).
23. V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, andG. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997).
24. S. Savrasov, G. Kotliar, andE. Abrahams, Nature (London) 410, 793 (2001);
25. S. Savrasov and G. Kotliar, Phys. Rev. Lett. 84, 3670 (2000).
26. G. Kotliar and S. Y. Savrasov, in New Theoretical Approaches to Strongly Correlated Systems, edited by A. M. Tsvelik (Kluwer Academic, Dordrecht, 2001).
27. For a review, see K. Held, I. A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A. K. McMahan, R. T. Scalettar, T. Pruschke, V. I. Anisimov, and D. Vollhardt, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, edited by J. Grotendorst, D. Marx, and A. Muramatsu, NIC Series Vol. 10 (NIC Directors, Forschungszentrum Jülich, 2002), p. 175.
28. J.E. Hirsch, Phys. Rev. Lett. 87, 206402 (2001).
29. M. Springer and F. Aryasetiawan, Phys. Rev. B 57, 4364 (2001).
30. N.E. Zein and V.P. Antropov, (unpublished).
31. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981), Chap. 5.
32. D.R. Hamann and S.B. Fahy, Phys. Rev. B 47, 1717 (1993).
33. Lars Hedin, Phys. Rev. 139, A796 (1965).
34. R. Pietig, R. Bulla, andS. Blawid, Phys. Rev. Lett. 82, 4046 (1999).
35. A. Ochiai, T. Suzuki, andT. Kasuya, J. Phys. Soc. Jpn. 59, 4129 (1990).
36. S. Mori, C.H. Chen, andS.-W. Cheong, Nature (London) 392, 473 (1998);
37. C.H. Chen and S.-W. Cheong, Phys. Rev. Lett. 76, 4042 (1996).
38. Y. Tomioka, A. Asamitsu, H. Kuwahara, andY. Tokura, J. Phys. Soc. Jpn. 66, 302 (1997).
39. J.B. Torrance, J.E. Vazquez, J.J. Mayerle, andV.Y. Lee, Phys. Rev. Lett. 46, 253 (1981);
40. Phys. Rev. Lett.J.B. Torrance, A. Girlando, J.J. Mayerle, J.I. Crowley, V.Y. Lee, andP. Batail, 47, 1747 (1981).
41. N. Nagaosa and J. Takimoto, J. Phys. Soc. Jpn. 55, 2735 (1986).
42. T. Egami, S. Ishihara, andM. Tachiki, Science 261, 1307 (1993);
43. S. Ishihara, T. Egami, andM. Tachiki, Phys. Rev. B 49, 8944 (1994);
44. Phys. Rev. BS. Ishihara, M. Tachiki, andT. Egami, 49, 16 123 (1994).
45. In E-DMFT, since the on-site interaction U does not get renormalized, one may find that the procedure of separating the Hartree contribution does not affect the result as far as the local interaction is concerned. So practically one can leave this term alone. The difference comes from the nonlocal interaction where the bare interaction vertex is replaced by an effective, on-site, and retarded one.
46. C. J. Bolech, S. S. Kancharla, andG. Kotliar, (unpublished).
47. J.W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Reading, MA, 1988), Chap. 2.
48. J.E. Hirsch and R.M. Fye, Phys. Rev. Lett. 56, 2521 (1986).
49. G.M. Buendia, Phys. Rev. B 33, 3519 (1986).
50. The overall accuracy of E-DMFT, which consists of the QMC solution of the impurity model and the self-consistent calculations, is of the order (formula presented) If not otherwise specified, all the data presented in this paper have an accuracy of (formula presented) The centers of the various symbols in the diagrams represent the locations of the data while their sizes do not reflect the accuracy. All functions of the Matsubara frequency are calculated at the corresponding discrete values. The lines connecting the points are guides to the eye.
51. In presenting the phonon-related results we always set (formula presented) A finite (formula presented) is used only in the QMC simulations.
52. S. Doniach and E.H. Sondheimer, Green’s Functions for Solid State Physicists (Benjamin, New York, 1974), Chaps. 6 and 7.
53. G. Strinati, H.J. Mattausch, andW. Hanke, Phys. Rev. Lett. 45, 290 (1980);
54. G. Strinati H.J. Mattausch W. HankePhys. Rev. B 25, 2867 (1982).
55. B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998).
56. C.-O. Almbladh, U. Von Barth, andR. Van Leeuwen, Int. J. Mod. Phys. B 13, 535 (1999).
57. A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewoods Cliffs, N.J. 1963), Sec. 10.
58. P. Nozieres, Theory of Interacting Fermi Systems (Addison-Wesley, Reading, MA, 1964), Chap. 3.
59. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).
60. L. Steinbeck, A. Rubio, L. Reining, M. Torrent, I.D. White, andR.W. Godby, Comput. Phys. Commun. 125, 105 (2000);
61. T.J. Pollehn, A. Schindlmayr, andR.W. Godby, J. Phys.: Condens. Matter 10, 1273 (1998).
62. S.S. Kancharla and C.J. Bolech, Phys. Rev. B 64, 085119 (2001).
63. We would like to thank Dr. S.S. Kancharla and Dr. C.J. Bolech for allowing us to use their DMRG programs for the calculation.
64. M.E. Torio, A.A. Aligia, andH.A. Ceccatto, Phys. Rev. B 64, R121105 (2001) and references therein.