Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations

TL;DR

This paper introduces a novel worm algorithm adapted for continuous-space PIMC simulations, enabling efficient analysis of large many-body quantum systems and their thermodynamic properties, exemplified by 2D Helium-4 superfluid transition.

Contribution

The paper extends the worm algorithm from lattice models to continuous-space systems, significantly improving simulation efficiency and system size scalability in PIMC methods.

Findings

Efficient computation of winding numbers and off-diagonal correlations.

Successful simulation of 2D Helium-4 superfluid transition.

Enhanced scalability over traditional PIMC methods.

Abstract

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC. As an illustrative application of the method, we simulate the superfluid transition of Helium-four in two dimensions.