Self-Consistent Many-Body Theory for Condensed Matter Systems

  • N. E. Bickers
Part of the CRM Series in Mathematical Physics book series (CRM)


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.


Renormalization Group Hubbard Model Vertex Function Condense Matter System Matsubara Frequency 
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