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From flat band ferromagnetism, we learned that the lowest energy half-filled flat band gives always ferromagnetism if the localized Wannier states on the flat band satisfy the connectivity condition. If the connectivity conditions are not satisfied, ferromagnetism does not appear. We show that this is not always the case namely, we show that ferromagnetism due to flat bands can appear even if the connectivity condition does not hold due to a peculiar behavior of the band situated just above the flat band. [ABSTRACT FROM AUTHOR]

Using a positive semidefinite operator technique we deduce exact ground states for a zig-zag hexagon chain described by a non-integrable Hubbard model with on-site repulsion. Flat bands are not present in the bare band structure, and the operators [image omitted], introducing the electrons into the ground state, are all extended operators and confined in the quasi-1D chain structure of the system. Consequently, by increasing the number of carriers, the [image omitted] operators become connected, i.e. touch each other on several lattice sites. Hence the spin projection of the carriers becomes correlated in order to minimize the ground-state energy by reducing as much as possible the double occupancy leading to a ferromagnetic ground state. This result demonstrates in exact terms in a many-body frame that the conjecture made at the two-particle level by G. Brocks et al., [Phys. Rev. 93 (2004) p.146405.] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes, is clearly viable, and opens up new directions in the search for routes in obtaining organic ferromagnetism. Due to the itinerant nature of the obtained ferromagnetic ground state, the systems under discussion may also have direct application possibilities in spintronics. [ABSTRACT FROM AUTHOR]