We study the ground state of a system of bosons interacting with Yukawa potentials, in both the liquid and solid phases, with a variational and an exact Monte Carlo method. A number of different wave functions to describe the solid phase are investigated. It is found that a Gaussian-Jastrow wave function has a lower energy than either a periodic wave function or a symmetrized Gaussian-Jastrow wave function. We have determined the liquid-solid coexistence curve and discovered that the solid melts when Lindemann's ratio exceeds 0.28. We have also determined that if the solid is superfluid, the superfluid fraction is less than 0.13. A significant conclusion of the comparison of exact and variational results is that the Gaussian-Jastrow wave function for a solid is better than the Jastrow function for liquid when used in a variational calculation. Thus a bias will be introduced when variational calculations are used to estimate crystallization and melting densities. There is a class of Yukawa potentials which do not have a crystalline phase at any density.

• Received 6 July 1977

DOI:https://doi.org/10.1103/PhysRevB.17.1070