A rigorous proof of the existence of band tails in disordered magnetic insulators

From the knowledge of the first moments of the density of states and, using a Lagrangian formalism, exact upper and lower bounds to the density of states of a simple hole in a magnetic insulator are calculated within the Hubbard model. These bounds provide a rigorous proof of the existence of band tails in the case of an antiferromagnetic spin arrangement in a simple cubic lattice. When the spin arrangement is random, the results suggest very strongly the existence of band tails.