Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

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.

9 pages and 3 figures. Submitted to J. Chem. Phys

References in corpus (2)

• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• 4He on a single graphene sheet

Cited by in corpus (15)

• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• Integral equation theory based dielectric scheme for strongly coupled electron liquids
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface
• Path Integral Monte Carlo study confirms a highly ordered snowball in 4He nanodroplets doped with an Ar+ ion
• Quantum phases of dipolar rotors on two-dimensional lattices
• Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function
• Onset temperature of Bose-Einstein condensation in incommensurate solid 4He
• Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
• Energy response and spatial alignment of the perturbed electron gas
• Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
• Exact kinetic propagators for coherent state complex Langevin simulations
• Combining Harmonic Sampling with the Worm Algorithm to Improve the Efficiency of Path Integral Monte Carlo