Ferromagnetism in the Extended Periodic Anderson Model Near Selective Mott Localization

Motivated by the experimental finding of Ferromagnetism (FM) near non-FL quantum phase transitions (QPT), I investigate FM in an Extended Periodic Anderson Model (EPAM). Using the Frobenius-Perron theorem, a FM {\it metallic} phase near the selective Mott localization is rigorously found. Interesting connections with Tasaki's flat-band ferromagnetism, as well as with the well-known double exchange (DE) mechanism are elucidated. This finding is a higher dimensional generalization of numerical work on the D=1 PAM, and constitutes a robust way to FM metallic behavior in $D>1$. Finally, we discuss a concrete manifestation of our results to $UGe_{2}$.