  We study the quantum phase transition in $f$-electron systems as a quantum
Lifshitz transition driven by selective Mott localization in a realistic
extended Anderson lattice model. Using DMFT, we find that a quantum critical
{\it phase} with anomalous $\omega/T$ scaling separates a heavy Landau-Fermi
liquid from ordered phase(s). Fermi surface reconstruction occurs via the
interplay between, and penetration of the Green function zeros to the poles,
leading to violation of Luttinger's theorem in the selective-Mott phase . We
show how this naturally leads to scale-invariant responses in transport. Our
work is represents a specific (DMFT) realization of the hidden-FL and FL$^{*}$
theories, and holds promise for study of "strange" metal phases in quantum
matter.
