We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transfered from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales. Introduction.-A widely-used method for dealing with interactions in strongly-correlated electron systems and electronic structure calculations is dynamical mean field theory (DMFT) [1,2]. It treats the interplay between a given lattice site (the "impurity") and the rest of the lattice (the "bath") as a quantum impurity model with a self-consistently determined hybridization function. Since DMFT's performance depends on that of the method used to solve this impurity model, much effort has been invested over the years to develop ever more powerful impurity solvers. For multi-band models, continuous-time Quantum Monte Carlo (ctQMC) methods appear to be the current favorites in terms of versatility and performance [3]. However, they are not without limitations: sign problems can occur, low-temperature calculations are costly, and obtaining real-frequency spectra requires analytic continuation of imaginary (Matsubara) frequency QMC data, which is notoriously difficult. Thus, there is a continued need for real-frequency impurity solvers suitable for multi-band DMFT applications.In this work, we show that the numerical renormalization group (NRG) [4-6] is such a tool, offering unprecedented real-frequency spectral resolution at low energies. NRG is the gold standard for impurity models, with numerous previous DMFT applications (e.g. [7][8][9][10][11][12][13]), but so far was limited to models with at most two bands. However, recent technical progress [14][15][16] has now made three-band calculations feasible [17][18][19].We illustrate the potential of DMFT+NRG by studying the minimal model [20][21][22] of a three-band "Hund's metal" [23,24], which has both a Hubbard interaction U and a ferromagnetic Hund's coupling J, with U(1) ch × SU(2) sp × SU(3) orb symmetry for its charge (ch), spin (sp) and orbital (orb) degrees of freedom. Hund's metals are multi-orbital materials with broad bands which are correlated via the Hund-J rather than the Hubbard-U interaction. Examples are iron pnictide and chalcogenide high-temperature superconductors [23,25], ruthen-

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Physical properties of multi-orbital materials depend not only on the strength of the effective interactions among the valence electrons but also on their type. Strong correlations are caused by either Mott physics that captures the Coulomb repulsion among charges, or Hund physics that aligns the spins in different orbitals. We identify four energy scales marking the onset and the completion of screening in orbital and spin channels. The differences in these scales, which are manifest in the temperature dependence of the local spectrum and of the charge, spin and orbital susceptibilities, provide clear signatures distinguishing Mott and Hund physics. We illustrate these concepts with realistic studies of two archetypal strongly correlated materials, and corroborate the generality of our conclusions with a model Hamiltonian study.