Abstract
We present a general formalism for the diagrammatic calculation of correlation functions for Hubbard-type models in terms of projected wave functions. It is shown that in the limit of high spatial dimensionsd only diagrams with bubble-structure remain. This causes correlation functions to have an overall RPA-type form ind→∞. Exact evaluations are performed for the Gutzwiller wave function. Nearest neighbor correlations are shown to be proportional to their value in the non-interacting case, i.e. are renormalized. However, their absolute value is only of order 1/d. Hence this wave function does not describe spin correlations adequately in high dimensions. The asymptotic behavior of the spin-correlation function is extracted and is found to have a scaling form similar tod=1. Assuming this form to hold in all dimensions we show that the Brinkman-Rice transition only occurs ind=∞. Finite orders of perturbation theory in 1/d around this singular point are not sufficient to remove the transition.
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van Dongen, P.G.J., Gebhard, F. & Vollhardt, D. Variational evaluation of correlation functions for lattice electrons in high dimensions. Z. Physik B - Condensed Matter 76, 199–210 (1989). https://doi.org/10.1007/BF01312685
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DOI: https://doi.org/10.1007/BF01312685