Correlated Lattice Fermions ind=∞Dimensions

Abstract

We show that even in $d=\infty$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3\mathrm{}$. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\infty$.