On the origin and convergence of a post-quantization constrained propagator for path integral simulations of rigid bodies

Abstract

We present a new methodological procedure, based on Post-Quantization Constraints (PQC), to obtain approximate density matrices and energy estimators for use in path integral molecular dynamics and Monte Carlo simulations. The approach serves as a justification of the use of "RATTLE & SHAKE" type methods for path integrals. A thorough discussion of the underlying geometrical concepts is given. Two standard model systems, the particle on a ring and the three-dimensional linear rotor, are used to illustrate and benchmark the approach. In these two cases, matrix elements of the newly defined propagator are explicitly computed in both "angular coordinate" and "angular momentum" bases. A detailed analysis of the convergence properties of the density matrix, and energy estimator with respect to their "exact" counterparts, is presented along with numerical illustrations. We conclude that the use of a PQC-type propagator is justified and practical.