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We generalize the linear discrete dimensional scaling approach for therepulsive Hubbard model to obtain a nonlinear scaling relation that yieldsaccurate approximations to the ground-state energy in both two and threedimensions, as judged by comparison to auxiliary-field quantum Monte Carlo(QMC) data. Predictions are made for the per-site ground-state energies in twoand three dimensions for $n$ (filling factor) and $U$ (Coulomb interaction)values for which QMC data are currently unavailable.

journal of physics. condensed matter

Approximate expression for the ground-state energy of the two- and  three-dimensional Hubbard model at arbitrary filling obtained from  dimensional scaling