  We have studied a two-dimensional triangular commensurate crystal of 4He with
the exact T=0 K Path Integral Ground State (PIGS) Monte Carlo method. We have
projected onto the true ground state both a Jastrow-Nosanow wave function, in
which equilibrium positions are explicitly given and no Bose-Einstein (BEC) is
present, and a translationally invariant shadow wave function, in which the
solid phase emerges through a spontaneously broken symmetry process and it has
BEC. We find a remarkable convergence to the same properties, both the diagonal
ones as well as the off-diagonal one-body density matrix rho_1. This supplies a
strong evidence that no variational bias are present in the PIGS method. We
find no BEC in the commensurate 2D 4He crystal at T=0 K, rho_1 shows an
exponential decay in the large distance range. The structure found in rho_1 is
due to virtual vacancy--interstitial pairs and this shows up in the momentum
distribution.
