  A practical experimental scheme for a quantum simulator of strongly
correlated electrons is proposed. Our scheme employs electrons confined in a
two dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface
acoustic waves are then induced in the GaAs substrate, which create a two
dimensional ``egg-carton'' potential. The dynamics of the electrons in this
potential is described by a Hubbard model with long-range Coulomb interactions.
The state of the electrons in this system can be probed via its conductance and
noise properties. This allows the identification of a metallic or insulating
state. Numerical estimates for the parameters appearing in the effective
Hubbard model are calculated using the proposed experimental system. These
calculations suggest that observations of quantum phase transition phenomena of
the electrons in the potential array are within experimental reach.
