The self-energy beyond GW: Local and nonlocal vertex corrections

Journal of Chemical Physics

Volumn 131, Issue 15, 2009, Pages

  Romaniello, P ^a,b   Guyot, S ^c   Reining, L ^a,b  

^a LABORATOIRE DES SOLIDES IRRADIÉS   (France)

^b European Theoretical Spectroscopy Facility ETSF   (France)

^c UNIVERSITÉ PARIS EST CRÉTEIL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGE SCREENING; CONDUCTION STATE; CORRELATED SYSTEMS; ELECTRON SELF-ENERGY; GW APPROXIMATION; NONLOCAL; SELF ENERGY; STRONGLY CORRELATED MATERIALS; THREE-POINT FUNCTION; TIME DEPENDENT DENSITY FUNCTIONAL THEORY; TWO-POINT; VERTEX CORRECTION;

ATOMS; DENSITY FUNCTIONAL THEORY;

ERROR CORRECTION;

EID: 70449428121     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3249965     Document Type: Article

References (59)

1. L. Hedin, Phys. Rev. 0096-8250 139, A796 (1965). 10.1103/PhysRev.139.A796
2. F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 0034-4885 61, 237 (1998), and references therein. 10.1088/0034-4885/61/3/002
3. W. G. Aulbur, L. Jonsson, and J. W. Wilkins, Solid State Physics (Academic, New York, 2000), Vol. 54, p. 1, and references therein.
4. G. Strinati, H. J. Mattausch, and W. Hanke, Phys. Rev. B 0163-1829 25, 2867 (1982). 10.1103/PhysRevB.25.2867
5. M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 0031-9007 55, 1418 (1985). 10.1103/PhysRevLett.55.1418
6. M. S. Hybertsen and S. G. Louie, Phys. Rev. B 0163-1829 34, 5390 (1986). 10.1103/PhysRevB.34.5390
7. R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. B 0163-1829 36, 6497 (1987). 10.1103/PhysRevB.36.6497
8. R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. B 0163-1829 37, 10159 (1988). 10.1103/PhysRevB.37.10159
9. L. Hedin, J. Phys.: Condens. Matter 0953-8984 11, R489 (1999). 10.1088/0953-8984/11/42/201
10. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 0034-6861 74, 601 (2002), and references therein. 10.1103/RevModPhys.74.601
11. G. D. Mahan and B. E. Sernelius, Phys. Rev. Lett. 0031-9007 62, 2718 (1989), and references therein. 10.1103/PhysRevLett.62.2718
12. Y. Takada, Phys. Rev. Lett. 0031-9007 87, 226402 (2001). 10.1103/PhysRevLett.87.226402
13. M. Hindgren and C. O. Almbladh, Phys. Rev. B 0163-1829 56, 12832 (1997). 10.1103/PhysRevB.56.12832
14. E. L. Shirley, Phys. Rev. B 0163-1829 54, 7758 (1996). 10.1103/PhysRevB.54.7758
15. P. Minnhagen, J. Phys. C 0022-3719 7, 3013 (1974). 10.1088/0022-3719/7/ 17/011
16. P. Minnhagen, J. Phys. C 0022-3719 8, 1535 (1975). 10.1088/0022-3719/8/ 10/010
17. A. Schindlmayr and R. W. Godby, Phys. Rev. Lett. 0031-9007 80, 1702 (1998). 10.1103/PhysRevLett.80.1702
18. C. Verdozzi, R. W. Godby, and S. Holloway, Phys. Rev. Lett. 0031-9007 74, 2327 (1995). 10.1103/PhysRevLett.74.2327
19. E. L. Shirley and R. M. Martin, Phys. Rev. B 0163-1829 47, 15404 (1993). 10.1103/PhysRevB.47.15404
20. R. Del Sole, L. Reining, and R. W. Godby, Phys. Rev. B 0163-1829 49, 8024 (1994). 10.1103/PhysRevB.49.8024
21. R. T. M. Ummels, P. A. Bobbert, and W. van Haeringen, Phys. Rev. B 0163-1829 57, 11962 (1998), and references therein. 10.1103/PhysRevB.57.11962
22. M. Springer, F. Aryasetiawan, and K. Karlsson, Phys. Rev. Lett. 0031-9007 80, 2389 (1998). 10.1103/PhysRevLett.80.2389
23. V. P. Zhukov, E. V. Chulkov, and P. M. Echenique, Phys. Rev. B 0163-1829 72, 155109 (2005). 10.1103/PhysRevB.72.155109 (Pubitemid 43024155)
24. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, (Benjamin, New York, 1964).
25. A. Schindlmayr, T. J. Pollehn, and R. W. Godby, Phys. Rev. B 0163-1829 58, 12684 (1998). 10.1103/PhysRevB.58.12684
26. P. Nozìres and C. T. Dedominicis, Phys. Rev. 0096-8250 178, 1097 (1969). 10.1103/PhysRev.178.1097
27. D. C. Langreth, Phys. Rev. B 0163-1829 1, 471 (1970). 10.1103/PhysRevB.1.471
28. B. Bergersen, F. W. Kus, and C. Blomberg, Can. J. Phys. 0008-4204 51, 102 (1973).
29. L. Hedin, Phys. Scr. 0031-8949 21, 477 (1980). 10.1088/0031-8949/21/3-4/ 039
30. A. S. Kheifets, V. A. Sashin, M. Vos, E. Weigold, and F. Aryasetiawan, Phys. Rev. B 0163-1829 68, 233205 (2003). 10.1103/PhysRevB.68.233205
31. R. A. Smith, Phys. Rev. A 1050-2947 46, 4586 (1992), and reference therein. 10.1103/PhysRevA.46.4586
32. F. Bruneval, F. Sottile, V. Olevano, R. Del Sole, and L. Reining, Phys. Rev. Lett. 0031-9007 94, 186402 (2005). 10.1103/PhysRevLett.94.186402 (Pubitemid 41493064)
33. R. Stubner, I. V. Tokatly, and O. Pankratov, Phys. Rev. B 0163-1829 70, 245119 (2004). 10.1103/PhysRevB.70.245119 (Pubitemid 40362436)
34. TDLDA has turned out to cover a big part of P, namely, contributions for nonvanishing momentum transfer q. We do not enter problems of time-ordering here, since, e.g., causal quantities can easily be obtained from time-ordered ones. We also use the fact that the relation between the measurable reducible polarizability and the irreducible P is well established.
35. M. Shishkin, M. Marsman, and G. Kresse, Phys. Rev. Lett. 0031-9007 99, 246403 (2007). 10.1103/PhysRevLett.99.246403 (Pubitemid 350276636)
36. J. Hubbard, Proc. R. Soc. London, Ser. A 0950-1207 276, 238 (1963). 10.1098/rspa.1963.0204
37. J. Hubbard, Proc. R. Soc. London, Ser. A 0950-1207 277, 237 (1964). 10.1098/rspa.1964.0019
38. W. Nelson, P. Bokes, P. Rinke, and R. W. Godby, Phys. Rev. A 1050-2947 75, 032505 (2007). 10.1103/PhysRevA.75.032505 (Pubitemid 46434361)
39. J. J. Fernandez, Phys. Rev. A 1050-2947 79, 052513 (2009). 10.1103/PhysRevA.79.052513
40. M. Taut, J. Phys. C 0022-3719 4, 9595 (1992).
41. X. Wang, C. D. Spataru, M. S. Hybertsen, and A. J. Mills, Phys. Rev. B 0163-1829 77, 045119 (2008). 10.1103/PhysRevB.77.045119
42. K. S. Thygesen and A. Rubio, Phys. Rev. 0096-8250 77, 11533 (2008).
43. 0 -1 represents essentially the quasiparticle shift. The two-point term f (1) contributes hence to the nonlocality correction Δ= f (1) +Δ ̃ defined in Eq.
44. R. W. Godby and M. Schlüter, Phys. Rev. Lett. 0031-9007 56, 2415 (1986). 10.1103/PhysRevLett.56.2415
45. M. Grüning, A. Marini, and A. Rubio, J. Chem. Phys. 0021-9606 124, 154108 (2006). 10.1063/1.2189226
46. M. Grüning, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 0021-9606 118, 7183 (2003). 10.1063/1.1562197
47. A. J. Cohen, P. Mori-Sanchez, and W. T. Yang, Science 0036-8075 321, 792 (2008). 10.1126/science.1158722
48. N. E. Dahlen, R. van Leeuwen, and U. von Barth, Phys. Rev. A 1050-2947 73, 012511 (2006). 10.1103/PhysRevA.73.012511 (Pubitemid 43270011)
49. A. Stan, N. E. Dahlen, and R. van Leeuwen, Europhys. Lett. 0295-5075 76, 298 (2006). 10.1209/epl/i2006-10266-6 (Pubitemid 44620859)
50. A. Schindlmayr, Phys. Rev. B 0163-1829 56, 3528 (1997). 10.1103/PhysRevB.56.3528
51. T. J. Pollehn, A. Schindlmayr, and R. W. Godby, J. Phys.: Condens. Matter 0953-8984 10, 1273 (1998). 10.1088/0953-8984/10/6/011
52. J. M. Tomczak, Ph.D. thesis, Ecole Polytechnique, 2007.
53. M. Puig von Friesen, C. Verdozzi, and C. -O. Almbladh, e-print arXiv:0905.2061v1.
54. We stress here that the electron-electron interaction U is spin independent, contrary to Uσ σ′ =U (1- δσ σ′), which is often used in the Hubbard model (Refs.). The constant U in Eq. corresponds to the localized limit of the many-body Hamiltonian as it is used in MBPT, hence it better reflects the approximations we want to examine. When acting on a Slater determinant, both choices yield the same result. This is not the case when the Hamiltonian acts on a generic state which is not antisymmetric. In this case, the spin-dependent interaction itself would take into account the Pauli principle, hence exchange-induced corrections.
55. U. von Barth and B. Holm, Phys. Rev. B 0163-1829 54, 8411 (1996) 10.1103/PhysRevB.54.8411; B. Holm and U. von Barth, Phys. Rev. B 0163-1829 57, 2108 (1998). 10.1103/PhysRevB.57.2108
56. A. Marini, R. Del Sole, A. Rubio, and G. Onida, Phys. Rev. B 0163-1829 66, 161104 (R) (2002). 10.1103/PhysRevB.66.161104
57. M. van Schilfgaarde, T. Kotani, and S. Faleev, Phys. Rev. Lett. 0031-9007 96, 226402 (2006). 10.1103/PhysRevLett.96.226402 (Pubitemid 43839566)
58. We choose the following convention as fermionic ordering: 〉 = c 2 c 1 c 1 00 〉.
59. In order to lift the degeneracy between the states 〉 and 〉 we can apply a magnetic field which stabilizes, for example, the state 〉.