Hund-projected Kanamori model: an effective description of Hund's metals near the Mott insulating regime

Abstract: Hund's coupling plays a decisive role in shaping electron correlations of multi-orbital systems, giving rise to a class of materials--Hund's metals--that combine local-moment physics with metallic transport. Here we derive an effective low-energy description of such a system near the Mott insulating regime, starting from the multi-orbital Hubbard-Kanamori Hamiltonian and projecting onto the high-spin manifold favored by Hund's first rule. The resulting Hund-projected Kanamori model captures the interplay between carrier motion and magnetic correlations in the presence of strong Hund's coupling. In the undoped limit, the model reduces to a spin-$N/2$ Heisenberg system with suppressed quantum fluctuations, approaching the classical limit for realistic five-band configurations. Upon doping, carrier motion couples strongly to the spin background and drives ferromagnetic correlations through a Hund-enhanced kinetic mechanism analogous to, but much stronger than, Nagaoka ferromagnetism. Owing to its reduced sign problem, the model can be addressed with advanced path-integral methods to determine quasiparticle structure and effective interactions between carriers-quantities that are challenging to obtain with other methods. This framework establishes a microscopic bridge between the Kanamori model and the emergent magnetic and transport phenomena characteristic of Hund's metals.