Quantum Virial Coefficients via Path Integral Monte Carlo with Semi-classical Beads

Abstract

Conventionally, Path Integral Monte Carlo (PIMC) calculations are performed with ‘classical beads’ (beads interacting via a classical potential) by using the primitive approximation for the thermal density matrix. Higher order propagators of the thermal density matrix have been proven to achieve faster convergence and better precision in quantum calculations than using just the primitive approximation. Use of different propagators in PIMC leads to methods equivalent to performing PIMC with ‘semi-classical beads’ (beads interacting via a semi-classical potential). We examine the Takahashi-Imada (TI) propagator as well as an ad hoc semi-classical potential in PIMC calculations for computing the quantum second virial coefficient for helium-4. We compare the performance of the two approaches based on semi-classical beads against values computed from PIMC using conventional classical beads. We find that while the TI propagator has the same or marginally better precision compared to the classical case, it has the best convergence rate (with respect to number of path-integral beads) among the three approaches. The convergence rate of the ad hoc potential is marginally better than its classical counterpart, and its precision is approximately the same as the classical case.