  Electron bands in the untwisted bilayer graphene flatten out in a transverse
electric field, offering a promising platform for correlated electron physics.
We predict that the spin/valley isospin magnetism, resembling that seen in
moir\'{e} bands, coexists with momentum-polarized phases occurring via a
``flocking transition'' in momentum space. This transition results in the
electron momentum distribution being spontaneously displaced relative to the
$K$ and $K'$ valley centers. These phases feature unusual observables such as
persistent currents in the ground state. Momentum-polarized carriers ``sample''
the Berry curvature of the conduction band, resulting in a unique behavior of
the anomalous Hall conductivity and other effects that do not occur in
previously studied systems.
