Density of states of the two-dimensional Hubbard model on a 4×4 lattice

Using exact diagonalization, we calculate the density of states of the two-dimensional Hubbard model on a 4×4 square lattice at U/t=0.5, 4, and 10, and even number of electrons with filling factors n ranging from a quarter filling up to half filling. We compare the ground-state energy and density of states at U/t=0.5 and 4 with second-order perturbation theory in U/t in the paramagnetic phase, and find that while the agreement is reasonable at U/t=0.5, it becomes worse as the perturbatively determined (i.e., using Stoner's criterion) boundary of the paramagnetic to spin-density-wave instability is approached. In the strong coupling regime (U/t=10), we find reasonable agreement between the density of states of the Hubbard and the t-J model especially for low doping fractions. In general, we find that at half filling the filled states are separated from the empty states by a gap. At U/t=10, the density of states shows two bands clearly separated by a Mott-Hubbard gap of order U.