Variational theory for correlated lattice fermions in high dimensions
- Cite this article as:
- Metzner, W. Z. Physik B - Condensed Matter (1989) 77: 253. doi:10.1007/BF01313669
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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.