  The repulsive Hubbard model on a sawtooth chain exhibits a lowest
single-electron band which is completely dispersionless (flat) for a specific
choice of the hopping parameters. We construct exact many-electron ground
states for electron fillings up to 1/4. We map the low-energy degrees of
freedom of the electron model to a model of classical hard dimers on a chain
and, as a result, obtain the ground-state degeneracy as well as closed-form
expressions for the low-temperature thermodynamic quantities around a
particular value of the chemical potential. We compare our analytical findings
with complementary numerical data. Although we consider a specific model, we
believe that some of our results like a low-temperature peak in the specific
heat are generic for flat-band ferromagnets.
