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

WH Ryu and YN Han and GA Voth, JOURNAL OF CHEMICAL PHYSICS, 150, 244103 (2019).

DOI: 10.1063/1.5097141

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. Published under
license by AIP Publishing.

Return to Publications page