Kondo frustration via charge fluctuations: a route to Mott localisation

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.