Path Integral Ground State study of 2D solid 4He

TL;DR

This study uses the Path Integral Ground State Monte Carlo method to investigate the ground state properties of a 2D solid helium-4 crystal, finding no evidence of Bose-Einstein condensation at zero temperature.

Contribution

It demonstrates the unbiased nature of the PIGS method by comparing results from different wave functions and confirms the absence of BEC in the 2D solid helium-4 at T=0 K.

Findings

No Bose-Einstein condensation observed in 2D solid 4He at T=0 K

Consistent properties obtained from different wave functions, indicating no variational bias

Presence of virtual vacancy-interstitial pairs affecting the momentum distribution

Abstract

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.