Properties of Hubbard models with degenerate localised single-particle eigenstates

Abstract

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 and where the projector onto the space of single-particle ground states is highly reducible. 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. We show how such lattices can be constructed in arbitrary dimensions. We construct all multi-particle ground states of these models for electron numbers not larger than the number of localised single-particle eigenstates. We derive some of the ground state properties, esp. the residual entropy, i.e. the finite entropy density at zero temperature.