  Strongly interacting systems are known to often spontaneously develop exotic
ground states under certain conditions. For instance, spin nematic phases have
been discovered in various magnetic models. Such phases, which break spin
symmetry but have no net local magnetization, have also been proposed by
Nersesyan et al. (J. Phys.: Cond. Matt. 3, 3353 (1991)) in the context of
electronic models. We introduce a N-flavor microscopic model that interpolates
from the large-N limit, where mean-field is valid and such a nematic phase
occurs, to the more realistic N=1 case. By using a sign-free quantum
Monte-Carlo, we show the existence of a spin nematic phase (analogous to a spin
flux phase) for finite N; when N decreases, quantum fluctuations increase and
this phase ultimately disappears in favor of an s-wave superconducting state.
We also show that this nematic phase extends up to a finite critical charge
doping. Dynamical studies allow us to clarify the Fermi surface property: in
the nematic phase at half-filling, it consists of 4 points and the low-energy
structure has a Dirac cone-like shape. Under doping, we observe clear
signatures of Fermi pockets around these points.
  This is one of the few examples where numerical simulations show how quantum
fluctuations can destroy a large-N phase.
