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 $n_d=2$, 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 $1<n_d<3$ and sizeable $J$. There orbital screening always occurs at much higher energies than spin screening below which Fermi-liquid behavior sets in. The low quasiparticle weight can then be directly explained in terms of the Hund's-coupling-reduced Fermi-liquid scale. We carefully analyze the effect of $J$ (Hundness), and the effect of the MIT at $n_d=2$ and $n_d=3$ (Mottness) on the energy scales and the nature of SOS. In the Hund-metal regime, far from any MIT, Hundness is shown to be the key player to induce strong correlations by constraining the spin rather than the charge dynamics. There, physical properties are governed by a broad incoherent energy regime of SOS where intriguing Hund metal physics occurs: large, almost unscreened spins are coupled to screened orbital degrees of freedom. With increasing proximity to an MIT correlations are further enhanced and the Fermi-liquid scale is further reduced. However, in the Hund-metal regime, this effect of Mottness is minor. In contrast, very close to the MIT at $n_d=2$, the incoherent spin–orbital separation regime is strongly downscaled and becomes negligibly small, whereas Mottness – the localization of charges – becomes dominant in inducing strong correlations. Close to the MIT at $n_d=3$, the SOS regime widens up because the orbital degrees of freedom get blocked by the formation of an $S=\frac{3}{2}$ impurity spin, but its nature changes: the orbital and spin dynamics get decoupled. Our results confirm Hundness as a distinct mechanism towards strong correlations in the normal state of Hund metals, leading to various interesting implications for the nature of electronic transport.