Path-integral ground-state Monte Carlo study of two-dimensional solidHe4

Abstract

We have studied a two-dimensional (2D) triangular commensurate crystal of $^{4}\mathrm{He}$ with the exact $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ 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 ${\ensuremath{\rho}}_{1}$. Thus, the commensurate 2D $^{4}\mathrm{He}$ crystal at $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is exactly solved, we find no Bose-Einstein condensation (BEC), and ${\ensuremath{\rho}}_{1}$ shows a dominant exponential decay in the large distance range. The structure found in ${\ensuremath{\rho}}_{1}$ is due to virtual vacancy-interstitial pairs and this shows up in the momentum distribution. Our result indicates that BEC in 2D solid $^{4}\mathrm{He}$ can only arise in the presence of some kind of disorder, either intrinsic or extrinsic.