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