Self-Consistent Many-Body Theory for Condensed Matter Systems
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Abstract
Self-consistent field techniques for the many-electron problem are examined using the modern formalism of functional methods. Baym-Kadanoff, or Φ-derivable, approximations are introduced first. After a brief review of functional integration results, the connection between conventional mean-field theory and higher-order Baym-Kadanoff approximations is established through the concept of the action functional. The Φ-derivability criterion for thermodynamic consistency is discussed, along with the calculation of free-energy derivatives. Parquet, or crossing-symmetric, approximations are introduced next. The principal advantages of the parquet approach and its relationship to Baym-Kadanoff theory are outlined. A linear eigenvalue equation is derived to study instabilities of the electronic normal state within Baym-Kadanoff or parquet theory. Finally, numerical techniques for the solution of self-consistent field approximations are reviewed, with particular emphasis on renormalization group methods for frequency and momentum space.
Keywords
Renormalization Group Hubbard Model Vertex Function Condense Matter System Matsubara FrequencyPreview
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15 References
- [1]G. Baym and L.P. Kadanoff, Phys. Rev. 124, 287 (1961).CrossRefADSMathSciNetzbMATHGoogle Scholar
- [2]G. Baym, Phys. Rev. 127, 1391 (1962).CrossRefADSzbMATHMathSciNetGoogle Scholar
- [3]C. de Dominicis and P.C. Martin, J. Math. Phys. 5, 14, 31 (1964).CrossRefADSGoogle Scholar
- [4]N.E. Bickers and D.J. Scalapino, Ann. Phys. (N.Y.) 193, 206 (1989).CrossRefADSGoogle Scholar
- [5]A more detailed discussion of the topics in Section 3 is available elsewhere. For a pedagogical treatment see, e.g., N.E. Bickers, The Large Degeneracy Expansion in Dilute Magnetic Alloys, Ph.D. thesis, Cornell University, 1986.Google Scholar
- [6]See, e.g., M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).CrossRefADSGoogle Scholar
- [7]Parts of our discussion below are an expansion of an earlier set of published lecture notes (N.E. Bickers, Int. J. Mod. Phys. 5, 253 (1991)).CrossRefADSGoogle Scholar
- [8]See, e.g., P. Nozières, Theory of Interacting Fermi Systems (W.A. Benjamin, New York, 1964).zbMATHGoogle Scholar
- [9]S. Babu and G.E. Brown, Ann. Phys. (N.Y.) 78, 1 (1973).CrossRefADSGoogle Scholar
- [10]M. Pfitzner and P. Wölfle, Phys. Rev. B35, 4699 (1987).ADSGoogle Scholar
- [11]K.F. Quader, K.S. Bedell, and G.E. Brown, Phys. Rev. B36, 156 (1987), and references therein.ADSGoogle Scholar
- [12]N.E. Bickers, D.J. Scalapino, and S.R. White, Phys. Rev. Lett. 62, 961 (1989).CrossRefADSGoogle Scholar
- [13]N.E. Bickers and S.R. White, Phys. Rev. B43, 8044 (1991).ADSGoogle Scholar
- [14]J.W. Serene and D.W. Hess, Phys. Rev. B44, 3391 (1991).ADSGoogle Scholar
- [15]L.G. Aslamazov and A.I. Larkin, Fiz. Tverd. Tela. 10, 1104 (1968). [English translation: Soviet Phys.—Solid State 10, 875 (1968).Google Scholar
- [16]C.-X. Chen, J. Luo, and N.E. Bickers, J. Appl. Phys. 69, 5469 (1991).CrossRefADSGoogle Scholar
- [17]C.-X. Chen and N.E. Bickers, Solid State Commun. 82, 311 (1992).CrossRefADSGoogle Scholar
- [18]C.-H. Pao and N.E. Bickers, Phys. Rev. Lett. 72, 1870 (1994); Phys. Rev. B51, 16310 (1995).CrossRefADSGoogle Scholar
- [19]P. Monthoux and D.J. Scalapino, Phys. Rev. Lett. 72, 1874 (1994).CrossRefADSGoogle Scholar
- [20]St. Lenck, J.P. Carbotte, and R.C. Dynes, Phys. Rev. B50, 10149 (1994).ADSGoogle Scholar
- [21]T. Dahm and L. Tewordt, Phys. Rev. Lett. 74, 793 (1995).CrossRefADSGoogle Scholar
- [22]J. Luo and N.E. Bickers, Phys. Rev. B47, 12153 (1993); Phys. Rev. B48, 15983 (1993).ADSGoogle Scholar
- [23]C.-H. Pao and N.E. Bickers, Phys. Rev. B49, 1586 (1994).ADSGoogle Scholar
- [24]C.-X. Chen and N.E. Bickers, unpublished.Google Scholar
- [25]G. Esirgen and N.E. Bickers, Phys. Rev. B55, 2122 (1997); Phys. Rev. B57, 5376 (1998).ADSGoogle Scholar
- [26]C.-H. Pao and H.-B. Schüttler, preprint, 1998.Google Scholar