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Hund metals are multi-orbital systems with moderate Coulomb interaction, $U$,and sizeable Hund's rule coupling, $J<U$, that aligns the spins in differentorbitals. They show strong correlation effects, like very low Fermi-liquidcoherence scales and intriguing incoherent transport regimes, resulting in badmetallic behavior. But to what extent are these strong correlations governed byMottness, i.e. the blocking of charge fluctuations close to a Mott insulatortransition (MIT) induced by $U$, or by Hundness, a new route towards strongcorrelations induced by $J$? To answer this question, we study the full phasediagram of a degenerate three-band Hubbard-Hund model on a Bethe lattice atzero temperature using single-site DMFT and the numerical renormalization groupas efficient real-frequency multi-band impurity solver. Hund metal behavioroccurs in this minimal model for a filling close to $n_d=2$, moderate $U$ andsizeable $J$, the "Hund-metal regime", with strong correlations manifest by alow quasiparticle weight, $Z$. We show that "spin-orbital separation" (SOS) isa generic $J$-induced feature in the whole metallic regime of the phase diagramfor $1<n_d<3$ and sizeable $J$: orbital screening occurs at much higherenergies than spin screening, below which Fermi-liquid behavior sets in. Thelow $Z$ can then be explained in terms of the $J$-reduced Fermi-liquid scale.We further show that, in the Hund-metal regime, far from any MIT, Hundness --the localization of large spins -- is the key player to induce strongcorrelations. There, physical properties are governed by a broad incoherentenergy regime of SOS with intriguing Hund metal physics: large, almostunscreened spins are coupled to screened orbital degrees of freedom.

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