Hubbard model on the infinite-dimensional diamond lattice

We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, ${\mathit{U}}_{\mathit{c}}$/t≊2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at ${\mathit{U}}_{\mathit{c}}$=0.