Global phase diagram of a Kondo Hund impurity model and the destruction of Fermi-liquid theory

In many correlated materials, notably the Hund metals, the Landau Fermi-liquid coherence scale T _FL is found to be very small. In this Letter, we interpret its smallness in terms of proximity to quantum critical points (QCPs): We use the numerical renormalization group (NRG) to compute the global phase diagram of the simplest three-channel spin-orbital Kondo impurity model capturing the essential physics of Hund metals. When the spin or spin-orbital Kondo couplings are tuned into the ferromagnetic regimes, we find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase, signalling the existence of QCPs, while T _FL is suppressed to zero. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^-1/5), orbital (ω^1/5) and spin-orbital (ω¹) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the NFL phase.