| We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single-particle ground states (flat band). To what extend a classification of the multi-particle ground states is possible, depends on the structure of the projector onto the space of the single-particle ground states. If the projector in lattice representation is irreducible, the system as a unique ferromagnetic ground state if the number of electrons is equal to the degeneracy. If it is reducible, the number and the properties of the multi-particle ground states can be determined by suitable combinations of the states within the irreducible subspaces. This means that one can find a basis in the space of the single-particle ground states such that the support of each single-particle ground state belongs to some small cluster and these clusters do not overlap. If the dimension of the irreducible subspaces is small, this allows a complete characterization of all multi-particle ground states and yields a residual entropy, i.e. a finite entropy density at zero temperature, which can be calculated. |
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