Hundness versus Mottness in a three-band Hubbard–Hund model: On the origin of strong correlations in Hund metals

Hund metals are multi-orbital systems with moderate Coulomb interaction, U, among charges and sizeable Hund’s rule coupling, J (< U) , that aligns the spins in different orbitals. They show strong correlation effects, like very low Fermi-liquid coherence scales and intriguing incoherent transport regimes, resulting in bad metallic behavior. But to what extent are these strong correlations governed by Mottness, i.e. the blocking of charge fluctuations close to a Mott insulator transition (MIT) induced by U, or by Hundness, a new route towards strong correlations induced by J? To answer this question, we study the full phase diagram of a degenerate three-band Hubbard–Hund model on a Bethe lattice at zero temperature using single-site dynamical mean-field theory and the numerical renormalization group as efficient real-frequency multi-band impurity solver. Hund metal behavior occurs in this minimal model for a filling close to nd = 2, moderate U and sizeable J, the “Hund-metal regime”. In particular, strong correlations manifest themselves there by an unusually low quasiparticle weight. Generalizing previous results on this model, we show that “spin–orbital separation” (SOS) is a generic Hund’s-coupling-induced feature in the whole metallic regime of the phase diagram for 1 < nd < 3 and sizeable J.