A Multigrid Algorithm for Sampling Imaginary-Time Paths in Quantum Monte Carlo Simulations

TL;DR

This paper introduces a multigrid algorithm combined with stochastic blocking to significantly improve the efficiency of sampling in quantum Monte Carlo simulations of imaginary-time paths, especially near the continuum limit.

Contribution

It presents a novel multigrid-based approach that overcomes the slowing-down problem in quantum Monte Carlo path sampling, enhancing ergodicity and computational speed.

Findings

Demonstrates improved sampling efficiency in one-dimensional quantum systems.

Shows reduction in simulation time compared to standard methods.

Validates the method's effectiveness across multiple test cases.

Abstract

We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid method to rapidly accelerate the sampling of paths in a quantum Monte Carlo simulation, making its dynamics more ergodic. The effectiveness and efficiency of this method are demonstrated for several one-dimensional quantum systems and compared to other standard and accelerated methods.