We review recent progress on the physics of electrons in the bilayered electron gas, relevant to coupled quantum wells in GaAs/AlGaAs heterostructures. First, we focus on the phase diagram of a symmetric bilayer at T=B=0, obtained by diffusion Monte Carlo simulations. It is found that inter–layer correlations stabilize crystalline structures at intermediate inter–layer separation, while favouring a liquid phase at smaller distance. Also, the available DMC evidence is in contrast with the recently (Hartree–Fock) predicted total charge transfer (TCT), whereby all the electron spontaneously jump in one layer. In fact, one can show that such a TCT state is never stable in the ideal bilayer with no tunneling. We finally comment on ongoing DMC investigations on the electron-hole bilayer, where excitonic condensation is expected to take place.
Modified Hartree-Fock-Bogoliubov theory at finite temperature