Hund Physics Landscape of Two-Orbital Systems

Motivated by the recent discovery of superconductivity in infinite-layer nickelates, we study the role of Hund coupling in a quarter-filled two-orbital Hubbard model, which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hund metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator, while the other three, which we call "intermediate" metal, weak Hund metal, and valence-skipping metal, from the effect of Hund coupling being away from Mottness. Defining criteria characterizing these metals is suggested, establishing the existence of Hund metallicity in two-orbital systems.