Diagrammatic Iteration Approach to Electron Correlation Effects

Affiliation(s)

Chongqing Center for Superconductive Science & Technology, Chongqing Academy of Science and Technology, Chongqing, China.

JD Duz Institute for Superconductivity, Baton Rouge, USA.

Chongqing Center for Superconductive Science & Technology, Chongqing Academy of Science and Technology, Chongqing, China.

JD Duz Institute for Superconductivity, Baton Rouge, USA.

ABSTRACT

Electron
correlation is a measure of the errors that are inherent in the Hartree-Fock theory
or orbital models. When the electron density is high, correlation is weak and
the traditional electronic theory works well. However, at a low density of
electrons correlation effects become strong and the traditional theory fails to
describe the electron system correctly. Therefore, the electron correlation plays
a radical role in such materials as high-temperature superconductors and heavy
fermions, etc. To date, there is no agreement on how to deal with higher-order
terms (correlation energy) in the series of electron’s ground state energy
although a method that is termed diagrammatic iteration approach (DIA) was
developed more than one decade ago by the authors of this article. That is why
no consensus on the origin and mechanism of superconductivity has been engaged
in superconductivity community. From the viewpoint of methodology, the DIA is
indeed an approach to higher-order terms from the lower-order ones, *i.e.* it is a new method to show how to
go beyond the random phase approximation (RPA) step by step by iteration. Here,
we are logically presenting it to the community of modern physics with more analyses
and hope to attract more attention to it and promote its applications.

KEYWORDS

Electron Correlation Effect, Diagrammatic Iteration Approach, Superconductivity, Condensed Matter Physics

Electron Correlation Effect, Diagrammatic Iteration Approach, Superconductivity, Condensed Matter Physics

Cite this paper

Fan, J. and Malozovsky, Y. (2014) Diagrammatic Iteration Approach to Electron Correlation Effects.*Journal of Modern Physics*, **5**, 549-561. doi: 10.4236/jmp.2014.57066.

Fan, J. and Malozovsky, Y. (2014) Diagrammatic Iteration Approach to Electron Correlation Effects.

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[1] Malozovsky, Y.M. and Fan, J.D. (1997) Superconductivity Science and Technology, 10, 259-277.

http://dx.doi.org/10.1088/0953-2048/10/5/002

[2] Mahan, G.D. (1991) Many-Particle Physics. 2nd Edition, Plenum, New York.

[3] Fan, J.D. and Malozovsky, Y.M. (2013) International Journal of Modern Physics B, 27, 1362035.

http://dx.doi.org/10.1142/S021797921362035X

[4] Schrieffer, J.R. (1964) Theory of Superconductivity. Benjamin Inc., New York.

[5] Fan, J.D. and Malozovsky, Y.M. (2001) Physica C, 101, 364-365. http://dx.doi.org/10.1016/S0921-4534(01)00723-7

[6] Fan, J.D. and Malozovsky, Y.M. (1999) International Journal of Modern Physics B, 13, 3505-3509.

http://dx.doi.org/10.1142/S0217979299003301

[7] Chakravarty, S. and Kivelson, S.A. (2001) Physical Review B, 64, 064511.

http://dx.doi.org/10.1103/PhysRevB.64.064511

[8] Chakravarty, S. and Kivelson, S. (1991) Europhsics Letters, 16, 751. http://dx.doi.org/10.1209/0295-5075/16/8/008

[9] Chakravarty, S., Gelfand, M.P. and Kivelson, S. (1991) Science, 254, 970.

http://dx.doi.org/10.1126/science.254.5034.970

[10] Baskaran, G. and Tosarit, E. (1991) Current Science, 61, 22.

[11] Gel-Mann, M. and Brueckner, K. (1957) Physical Review, 106, 364. http://dx.doi.org/10.1103/PhysRev.106.364

[12] Sawada, K., Brueckner, K.A., Fukuda, N. and Brout, R. (1957) Physical Review, 108, 507.

http://dx.doi.org/10.1103/PhysRev.108.507

[13] Hubbard, J. (1957) Proceedings of the Royal Society A, 243, 336. http://dx.doi.org/10.1098/rspa.1958.0003

[14] Nozieres, P. and Pines, D. (1958) Physical Review, 111, 442. http://dx.doi.org/10.1103/PhysRev.111.442

[15] Quinn, J.J. and Ferrell, A. (1958) Physical Review, 112, 812. http://dx.doi.org/10.1103/PhysRev.112.812

[16] Isihara, A. (1984) Solid State Physics, 42, 271-402.

[17] (a) Eliashberg, G.M. (1960) Soviet Physics—JETP, 11, 696.

(b) Eliashberg, G.M. (1960) Soviet Physics—JETP, 12, 1000.

[18] Abrikosov, A.A., Gorkov, L.P. and Dzyaloshinski, I.E. (1964) Method of Quantum Field Theory in Statistical Physics. Prentice-Hall, New Jersey.

[19] Migdal, A.B. (1958) Soviet Physics JETP, 34, 996.

[20] Engelsberg, S. and Schrieffer, J.R. (1963) Physical Review, 131, 993. http://dx.doi.org/10.1103/PhysRev.131.993

[21] Nozieres, P. (1964) Theory of Interacting Fermi System. W.A. Benjamin, Inc.

[22] Gorkov, L.P. and Melik-Barkhudarov, T.K. (1961) Soviet Physics—JETP, 12, 1018.

[23] Grabowski, M. and Sham, L.J. (1984) Physical Review, B29, 6132. http://dx.doi.org/10.1103/PhysRevB.29.6132