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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]

A technique based on the transformation in positive semidefinite form of the Hamiltonian (Ĥ) is developed to allow the study of the enlargement possibilities of the emergence domain of a given state. For this reason the calculation of exact ground states for the polyphenylene type of non-integrable chains is performed. Using different exact transcriptions of Ĥ in positive semidefinite form and different solutions of the matching equations, the same type of ground state is deduced in different regions of the parameter space, hence a more global view of its emergence possibilities is obtained. With this procedure an enlarged view of the appearance in the phase diagram of different studied phases can be achieved. [ABSTRACT FROM PUBLISHER]