Coarse-graining of many-body path integrals: Theory and numerical approximations

Feynman's imaginary time path integral approach to quantum statistical mechanics provides a theoretical formalism for including nuclear quantum effects (NQEs) in simulation of condensed matter systems. Sinitskiy and Voth [J. Chem. Phys. 143, 094104 (2015)] have presented the coarse-grained path integral (CG-PI) theory, which provides a reductionist coarse-grained representation of the imaginary time path integral based on the quantum-classical isomorphism. In this paper, the many-body generalization of the CG-PI theory is presented. It is shown that the N interacting particles obeying quantum Boltzmann statistics can be represented as a system of N pairs of classical-like pseudoparticles coupled to each other analogous to the pseudoparticle pair of the one-body theory. Moreover, we present a numerical CG-PI (n-CG-PI) method applying a simple approximation to the coupling scheme between the pseudoparticles due to numerical challenges of directly implementing the full many-body CG-PI theory. Structural correlations of two liquid systems are investigated to demonstrate the performance of the n-CG-PI method. Both the many-body CG-PI theory and the n-CG-PI method not only present reductionist views of the many-body quantum Boltzmann statistics but also provide theoretical and numerical insight into how to explicitly incorporate NQEs in the representation of condensed matter systems with minimal additional degrees of freedom.