Linked cluster expansion of the many-body path integral

We develop an approach of calculating the many-body path integral based on the linked cluster expansion method. First, we derive a linked cluster expansion and we give the diagrammatic rules for calculating the free energy and the pair distribution function g(r) as a systematic power-series expansion in the particle density. We also present a structured Padé approximation scheme in the momentum space to determine g(r). The calculated g(r) for distinguishable particles interacting with Lennard-Jones and hard-sphere potential in various attempted schemes of approximation of the diagrammatic series compares very well with the results of path-integral Monte Carlo simulation. Our method is applicable to a wide range of problems of current general interest and may be extended to the case of identical particles and, in particular, to the case of the many-fermion problem. © 2019 American Physical Society.