We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\sim}{|\ensuremath{\omega}|}^{r}$, with exponent $\ensuremath{-}1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents
r and $(\ensuremath{-}r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.
Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) $({\ensuremath{\rho}}_{c}(\ensuremath{\omega})={\ensuremath{\rho}}_{0}/{|\ensuremath{\omega}|}^{r}, 0<r<1)$ in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling, termed power-law diverging multichannel Kondo model. This model considers
M channel and
N spin degrees of freedom. Employing a renormalization group analysis and dynamical large-
N approach, our results reveal the emergence of a pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. We precisely determine the conditions under which the pseudogap behavior occurs, either by tuning the exponent
r or the ratio $\ensuremath{\kappa}=M/N$ to values such as
r∗ or ${\ensuremath{\kappa}}^{*}$. This pseudogap phase of spinon exhibits distinct physical properties that could have an impact on the properties of real systems. The results of this study provide novel insights into the pseudogap behaviors in strongly correlated systems and offer a playground to study the interplay between higher-order van Hove singularities and multichannel Kondo physics.
Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. 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 (ω^{1}) 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 non-Fermi-liquid phase.