Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

TL;DR

This paper introduces a new class of high-order propagators for path-integral Monte Carlo simulations, enabling more accurate and efficient quantum many-body system computations by subtracting lower order propagators and maintaining positivity.

Contribution

The authors develop a novel extrapolation method for high-order imaginary time propagators that can achieve arbitrary order accuracy in path-integral Monte Carlo simulations.

Findings

Achieved fourth, sixth, and eighth order convergence in simulations of quantum many-body systems.

Demonstrated negligible impact of positivity violations at small time steps.

Validated the method on bulk liquid helium-4.

Abstract

We present a new class of high-order imaginary time propagators for path-integral Monte Carlo simulations by subtracting lower order propagators. By requiring all terms of the extrapolated propagator be sampled uniformly, the subtraction only affects the potential part of the path integral. The negligible violation of positivity of the resulting path integral at small time steps has no discernable affect on the accuracy of our method. Thus in principle arbitrarily high order algorithms can be devised for path-integral Monte Carlo simulations. We verify this claim is by showing that fourth, sixth, and eighth order convergence can indeed be achieved in solving for the ground state of strongly interacting quantum many-body systems such as bulk liquid $^4$He.