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We consider the repulsive Hubbard model on several lattices (including sawtooth chain, diamond chain or square-kagom\' lattice) which support dispersionless (flat) one-electron bands. Inspiring by previous studies on the Heisenberg antiferromagnets [1] we construct exact many-electron ground states for low electron densities, map the low-energy degrees of freedom of the electron model to a model of classical hard dimers, 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. (Some details of calculations for the sawtooth Hubbard chain can be found in Ref. 2.) All considered electron models exhibit a universal behavior. We also discuss magnetic properties of the considered models which under certain conditions may exhibit ground-state ferromagnetism. We compare our analytical findings with complementary numerical data for finite systems.
These studies were performed in collaboration with J. Richter (Magdeburg) and A.Honecker (Göttingen). [1] J.Schulenburg et al, Phys.Rev.Lett. 88, 167207 (2002). [2] O.Derzhko, A.Honecker, and J.Richter, Phys.Rev.B 76, 220402(R) (2007). |
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