Derzhko, OlegOlegDerzhkoRichter, J.J.RichterHonecker, AndreasAndreasHoneckerMaksymenko, M.M.MaksymenkoMoessner, R.R.Moessner2018-11-072018-11-072010https://resolver.sub.uni-goettingen.de/purl?gro-2/21212We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices-saw-tooth chain and two kagome chains-with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of exact many-electron ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential mu(0). We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact-diagonalization data for finite systems.journal_article10.1103/PhysRevB.81.014421000274001800063