The Anderson-Hubbard (A-H) model with one or two holes and with periodic boundary conditions on a 4Mx 4N square lattice is considered. On grounds of an intuitive generalization of Marshall's theorem we split the A-H Hamiltonian (HA−H) into a zeroth order term (H0) and a perturbation term (H'). With H0 we construct unfrustrated states: the zeroth order approximation of the degenerate ground state (GS). The one-hole system has a four-fold symmetry broken H0-GS with k = (π/2, ±π/2), (-π/2, ±π/2). Group theory shows that this symmetry breaking (SB) may be stable if H' is taken into account. For the two-hole system we derive candidates for the H0-GS with the corresponding good quantum numbers k and total spin S. Here we find no SB or a two-fold SB: again, this result may hold for the complete HA−H. Second order perturbation calculation possibly describes an effective coupling of two holes.
