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Itinerant ferromagnetism is intrinsically a strongly correlated phenomenon, which remains a major challenge of condensed matter physics. Most ferromagnetic metals are orbital-active with prominent Hund’s coupling. However, the local physics of Hund’s rule usually does not lead to the ferromagnetic long-range order. Furthermore, the magnetic phase transitions of itinerant electrons are also difficult to handle by perturbative methods. In this talk, I will present non-perturbative studies on itinerant ferromagnetism. Exact theorems are established for a stable itinerant ferromagnetic phase in a large region of electron densities in multi-orbital systems, which provide sufficient conditions for Hund’s rule to build up global ferromagnetic coherence. In addition, thermodynamic properties and magnetic phase transitions of itinerant electrons are studied via sign-problem-free quantum Monte Carlo simulations at generic fillings. Without introducing local moments as a priori, the “Curie-Weiss metal” behavior is identified in a wide range of temperature. These results will provide useful guidance to current experimental search for novel itinerant ferromagnetic states in a large class of systems ranging from the transition-metal-oxide heterostructures (e.g. LaAlO3/SrTiO3) to the p-orbital bands in optical lattices filled with ultra-cold fermions.
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