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Highly frustrated lattices yield a completely flat lowest single-electronband. Remarkably, exact many-body ground states can be constructed for therepulsive Hubbard model and the t-J model by filling this flat band withlocalized electron states. This construction leads to a macroscopicground-state degeneracy. We discuss how to compute these ground-statedegeneracies for a certain class of models, including in particular thesawtooth chain. Furthermore, we discuss generic consequences forlow-temperature thermodynamic properties, like the appearance of alow-temperature peak in the specific heat. Finally, we present complementarynumerical results obtained by exact diagonalization.

Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices