Path-integral Monte Carlo worm algorithm for Bose systems with periodic boundary conditions

TL;DR

This paper presents a detailed description of a path-integral Monte Carlo worm algorithm tailored for Bose systems with periodic boundary conditions, enabling accurate thermodynamic calculations without move length limitations.

Contribution

The paper introduces a fully consistent worm algorithm for Bose systems with periodic boundaries that improves sampling efficiency and accuracy in thermodynamic simulations.

Findings

Validated against non-interacting Bose gas with exact results

Addresses convergence issues in high-density hard sphere systems

Ensures detailed balance without ambiguity in periodic images

Abstract

We provide a detailed description of the path-integral Monte Carlo worm algorithm used to exactly calculate the thermodynamics of Bose systems in the canonical ensemble. The algorithm is fully consistent with periodic boundary conditions, that are applied to simulate homogeneous phases of bulk systems, and it does not require any limitation in the length of the Monte Carlo moves realizing the sampling of the probability distribution function in the space of path configurations. The result is achieved adopting a representation of the path coordinates where only the initial point of each path is inside the simulation box, the remaining ones being free to span the entire space. Detailed balance can thereby be ensured for any update of the path configurations without the ambiguity of the selection of the periodic image of the particles involved. We benchmark the algorithm using the non-interacting Bose gas model for which exact results for the partition function at finite number of particles can be derived. Convergence issues and the approach to the thermodynamic limit are also addressed for interacting systems of hard spheres in the regime of high density.