A cellular dynamical mean field theory approach to Mottness

We investigate the properties of a strongly correlated electron system in the proximity of a Mott insulating phase within the Hubbard model, using a cluster generalization of the dynamical mean field theory. We find that Mottness is intimately connected with the existence in momentum space of a surface of zeros of the single particle Green’s function. The opening of a Mott-Hubbard gap at half filling and the opening of a pseudogap at finite doping are necessary elements for the existence of this surface. At the same time, the Fermi surface may change topology or even disappear. Within this framework, we provide a simple picture for the appearance of Fermi arcs. We identify the strong short-range correlations as the source of these phenomena and we identify the cumulant as the natural irreducible quantity capable of describing this short-range physics. We develop a new version of the cellular dynamical mean field theory based on cumulants that provides the tools for a unified treatment of general lattice Hamiltonians.