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Quadratic operators are used in transforming the model Hamiltonian (H) of onecorrelated and dispersive band in an unique positive semidefinite form cooptingboth the kinetic and interacting part of H. The expression is used in deducingexact ground states which are minimum energy eigenstates only of the fullHamiltonian. It is shown in this frame that at half filling, also dispersivebands can provide ferromagnetism in exact terms by correlation effects .

Quadratic operators used in deducing exact ground states for correlated systems: ferromagnetism at half filling provided by a dispersive band