Shadow wave-function variational calculations of crystalline and liquid phases ofHe4

A new class of variational wave functions for boson systems, shadow wave functions, is used to investigate the properties of solid and liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The wave function is translationally invariant and symmetric under particle interchange. In principle, the calculations for the crystalline phase do not require the use of any auxiliary lattice. Using the Metropolis Monte Carlo algorithm, we show that the additional variational degrees of freedom in the wave function lower the energy significantly. This wave function also allows the crystalization of an equilibrated liquid phase when a crystalline seed is used. The pair correlation function and structure factor S(k) are determined in the liquid phase. The condensate fraction is calculated as well. Results are given for the single-particle distribution function around the lattice positions in the solid phase.