Path-integral ground-state Monte Carlo study of two-dimensional solid 4He

We have studied a two-dimensional (2D) 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 two qualitatively different wave functions, a Jastrow-Nosanow wave function and a translationally invariant shadow wave function. The PIGS method passes this hard test of validity and applicability by obtaining the convergence to the same properties, both the diagonal ones as well as the off-diagonal one-body density matrix p1. Thus, the commensurate 2D 4He crystal at T=0 K is exactly solved, we find no Bose-Einstein condensation (BEC), and p1 shows a dominant exponential decay in the large distance range. The structure found in p1 is due to virtual vacancy-interstitial pairs and this shows up in the momentum distribution. Our result indicates that BEC in 2D solid 4He can only arise in the presence of some kind of disorder, either intrinsic or extrinsic.