Zeitschrift für Physik B Condensed Matter

, Volume 77, Issue 2, pp 253–266

Variational theory for correlated lattice fermions in high dimensions

  • Walter Metzner

DOI: 10.1007/BF01313669

Cite this article as:
Metzner, W. Z. Physik B - Condensed Matter (1989) 77: 253. doi:10.1007/BF01313669


A diagrammatic approach to the evaluation of correlated variational wave functions for strongly interacting fermions is presented. Diagrammatic rules for the calculation of the one-particle density matrix and the Hubbard interaction are derived which are valid for arbitraryd-dimensional lattices. An exact evaluation of expectation values is performed in the limitd=∞. The wellknown Gutzwiller approximation is seen to become the exact result for the expectation value of the Hubbard Hamiltonian in terms of the Gutzwiller wave function ind=∞. An efficient procedure to correct the Gutzwiller approximation in finite dimensions is developed. A detailed discussion of expectation values ind=∞ in terms of explicit antiferromagnetic wave functions is given. Thereby an approximate result for the ground state energy of the Hubbard model, obtained recently within a slave-boson approach, is recovered.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Walter Metzner
    • 1
  1. 1.Institut für Theoretische Physik CTechnische Hochschule AachenAachenFederal Republic of Germany