Hubbard and Anderson models on perovskitelike lattices: Exactly solvable cases

Abstract

Exact solutions of the Hubbard model and the periodic Anderson model in the limit of infinite interaction strength are presented. Both models are studied on a D-dimensional decorated hypercubic lattice with periodic boundary conditions for any dimension D\ensuremath{\ge}2 and arbitrary size. The lattice is very similar to the perovskite lattice. In addition to the ground-state energy, a corresponding eigenstate is constructed. This ground state contains at least two particles per unit cell. For the Anderson model, the exact solution is restricted to a surface in the (${\mathit{E}}_{\mathit{f}}$,V) parameter space; however, the resulting relation V(${\mathit{E}}_{\mathit{f}}$) does not lead to unphysical parameters.