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.
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Bickers, N.E. (2004). Self-Consistent Many-Body Theory for Condensed Matter Systems. In: Sénéchal, D., Tremblay, AM., Bourbonnais, C. (eds) Theoretical Methods for Strongly Correlated Electrons. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-21717-7_6
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DOI: https://doi.org/10.1007/0-387-21717-7_6
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