  We develop a unified theoretical picture for excitations in Mott systems,
portraying both the heavy quasiparticle excitations and the Hubbard bands as
features of an emergent Fermi liquid state formed in an extended Hilbert space,
which is non-perturbatively connected to the physical system. This observation
sheds light on the fact that even the incoherent excitations in strongly
correlated matter often display a well defined Bloch character, with pronounced
momentum dispersion. Furthermore, it indicates that the Mott point can be
viewed as a topological transition, where the number of distinct dispersing
bands displays a sudden change at the critical point. Our results, obtained
from an appropriate variational principle, display also remarkable quantitative
accuracy. This opens an exciting avenue for fast realistic modeling of strongly
correlated materials.
