Variational path-integral theory of thermal properties of solids

Abstract

We show that the Feynman path-integral formulation of the quantum many-body problem, when combined with a quadratic trial action whose parameters are determined variationally, leads to a partition function with a temperature- and volume-dependent effective potential that can easily be evaluated by the classical Monte Carlo method. This leads directly to reliable thermal properties of solids over a wide range of volumes and temperatures. To demonstrate the power of this theory, we apply it to Mie–Lennard-Jones crystals. We compare the results systematically with predictions of anharmonic and self-consistent lattice dynamics as well as classical Monte Carlo calculations. The results of this theory agree with the former ones, where they are applicable, for a wide range of volumes and from T=0 K to melting. This method should be regarded as an alternative to the quantum Monte Carlo approach for most quantum solids, since it is reliable and requires much less computer time.