Monte Carlo studies of two-dimensional phases of helium using a shadow wave function

Abstract

The solid and liquid phases of two-dimensional ${}^{4}\mathrm{He}$ are studied in detail using a variational ``shadow'' wave function. This wave function provides a unified description of both phases; spontaneous crystallization from a disordered initial state occurs in the solid phase. We have investigated the properties of the solid phase in detail and find that it lacks long range translational order, has a high density of defects, and low angular order relative to classical two-dimensional solids. These results are very similar to results obtained from simulations of a quantum hard disk system. We have also computed these properties for the liquid phase. These properties vary rapidly in the transition region and serve as a good signal for the transition itself.