Padé resummation of the linked cluster expansion of the many-particle path-integral.

We have developed a quantum cluster expansion, analogous to the well-known Mayer cluster expansion for the classical partition function and the pair distribution function, and a quantum version of the virial expansion by starting from the many-body path-integral. We first derive the diagrammatic series expansion for the pair distribution function and show that the expansion is linked. This expansion can also be thought of as a power series expansion in the particle density. To resum the series, we use a Padé approximation scheme in momentum space, which is constrained to yield the calculated order by order expansion terms and the classical limit correctly. We have tested the approach on a Lennard-Jones and a hard-sphere system and our results agree very well with those obtained from the path-integral Monte Carlo. Our method has immediate application to the case of short-range hard-core potential where the established analytical and semi-analytical tools of many-body perturbation theory and quantum statistical mechanics cannot be applied in a straightforward manner.