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We propose a minimal effective impurity model that captures the phenomenologyof the Mott-Hubbard metal-insulator transition (MIT) of the half-filled Hubbardmodel on the Bethe lattice in infinite dimensions as observed by dynamical meanfield theory (DMFT). This involves extending the standard Anderson impuritymodel Hamiltonian to include an explicit Kondo coupling $J$, as well as a localon-site correlation $U_b$ on the conduction bath site connected directly to theimpurity. For the case of attractive local bath correlations ($U_{b}<0$), theextended Anderson impurity model (e-SIAM) sheds new light on several aspects ofthe DMFT phase diagram. For example, the $T=0$ metal-to-insulator quantum phasetransition (QPT) is preceded by an excited state quantum phase transition(ESQPT) where the local moment eigenstates are emergent in the low-lyingspectrum. Long-ranged fluctuations are observed near both the QPT and ESQPT,suggesting that they are the origin of the quantum critical scaling observedrecently at high temperatures in DMFT simulations. The $T=0$ gaplessexcitations at the QCP display particle-hole interconversion processes, andexhibit power-law behaviour in self-energies and two-particle correlations.These are signatures of non-Fermi liquid behaviour that emerge from the partialbreakdown of the Kondo screening.

Kondo frustration via charge fluctuations: a route to Mott localisation