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

Abstract

Hund metals are multi-orbital systems with moderate Coulomb interaction, $U$, 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 DMFT 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", with strong correlations manifest by a low quasiparticle weight, $Z$. We show that "spin-orbital separation" (SOS) is a generic $J$-induced feature in the whole metallic regime of the phase diagram for $1<n_d<3$ and sizeable $J$: orbital screening occurs at much higher energies than spin screening, below which Fermi-liquid behavior sets in. The low $Z$ 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 strong correlations. There, physical properties are governed by a broad incoherent energy regime of SOS with intriguing Hund metal physics: large, almost unscreened spins are coupled to screened orbital degrees of freedom.