  Though most fermionic Mott insulators order at low temperatures, ordering is
ancillary to their insulating behaviour. Our emphasis here is on disentangling
ordering from the intrinsic strongly correlated physics of a doped half-filled
band. To this end, we focus on the 2D Hubbard model. Because the charge gap
arises from on-site correlations, we implement a non-perturbative approach
which incorporates local physics. Crucial to this method is a self-consistent
two-site dynamical cluster expansion which builds in the nearest-neighbour
energy scale, $J$.
  At half-filling, we find that the spectral function possesses a gap of order
$U$ and is devoid of any coherent quasi-particle peaks. In the doped case, we
find that the Fermi surface exceeds the Luttinger volume. Additionally in the
underdoped regime, we find that a pseudogap opens in the single particle
density of states.The pseudogap closes above optimal doping and hence our
proposal is not inconsistent with that of Loram. In analogy with the Mott gap
and antiferromagnetism, we propose that ordering may also accompany the
formation of a pseudogap. We suggest a current pattern within a 1-band model
that preserves translational but breaks time-reversal symmetry along the
canonical x and y axes but not along $x=\pm y$ that is consistent with the
experimental observations. Finally, we show that the Hall coefficient in a
doped Mott insulator must change sign at a doping level $x<1/3$. The sign
change is tied to a termination of strong correlation physics in the doped Mott
state.

Strongly Correlated Electrons