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

Highly frustrated lattices yield a completely flat lowest single-electron band. Remarkably, exact many-body ground states can be constructed for the repulsive Hubbard model and the t-J model by filling this flat band with localized electron states. This construction leads to a macroscopic ground-state degeneracy. We discuss how to compute these ground-state degeneracies for a certain class of models, including in particular the sawtooth chain. Furthermore, we discuss generic consequences for low-temperature thermodynamic properties, like the appearance of a low-temperature peak in the specific heat. Finally, we present complementary numerical results obtained by exact diagonalization.