  We theoretically consider bilayers of two dimensional (2D) electron gases as
in semiconductor quantum wells, and investigate possible spontaneous symmetry
breaking transitions at low carrier densities driven by interlayer Coulomb
interactions. We use a self-consistent technique implementing mean field
truncations of the interacting four-fermion terms, and find a U(1) layer
symmetry breaking transition at low carrier densities where the individual
layer identities are lost leading to an effective pseudospin XY ferromagnet in
the 2D plane. Our results validate earlier theoretical works using simpler
restricted Hartree-Fock techniques, and establish the pseudospin XY ferromagnet
as a possible low-density symmetry broken phase of 2D bilayers.
