  Semiconductor artificial graphene nanostructures where Hubbard model
parameter $U/t$ can be of the order of 100, provide a highly controllable
platform to study strongly correlated quantum many-particle phases. We use
accurate variational and diffusion Monte Carlo methods to demonstrate a
transition from antiferromagnetic to metallic phases for experimentally
accessible lattice constant $a=50$ nm in terms of lattice site radius $\rho$,
for finite sized artificial honeycomb structures nanopatterned on GaAs quantum
wells containing up to 114 electrons. By analysing spin-spin correlation
functions for hexagonal flakes with armchair edges and triangular flakes with
zigzag edges, we show that edge type, geometry and charge nonuniformity affect
the steepness and the crossover $\rho$ value of the phase transition. For
triangular structures, the metal-insulator transition is accompanied with a
smoother edge polarization transition.
