Comparative study of a model quantum solid using quantum Monte Carlo, the effective potential, and improved self-consistent theories

Abstract

We have used the quantum Monte Carlo formalism to calculate the volume, pressure, and energy at three temperatures for a nearest-neighbor Lennard-Jones solid, with parameters appropriate to solid neon. The purpose is to provide accurate test data for a system with substantial quantum effects. The results are compared with the predictions of the effective potential and improved self-consistent theories. The agreement of all three techniques is good. The effective-potential method results agree better with the quantum Monte Carlo results at high temperatures, and those of the improved self-consistent method agree better with the quantum Monte Carlo results at low temperatures. The relationship between the three theories is discussed. We show that at zero degrees the effective-potential method is equivalent to first-order self-consistent theory.