  The ground state phase diagram of the two-dimensional attractive Hubbard
model with population imbalance is explored using a mean field ansatz. A linear
programming algorithm is used to identify the blocked states, such that the
population imbalance can be imposed exactly. This allows to explore regions of
the number-projected phase diagram that can not be obtained with the
conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov
(FFLO) phase of pairs with non-zero momentum is found to be the ground state
over a wide range of parameters, while phase separation occurs only in a
limited region at small population imbalance. Through a particle-hole
transformation these results can be related to the underdoped repulsive Hubbard
model, where the FFLO phase takes the form of a particle-hole condensate that
exhibits a spontaneous restoration of spin symmetry.
