Physics – Condensed Matter
Scientific paper
1995-07-12
Phys. Rev. B 52, 17119 (1995)
Physics
Condensed Matter
17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate files
Scientific paper
10.1103/PhysRevB.52.17119
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.
Janis Vaclav
Schlipf Jan
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