Path-Integral Monte Carlo Worm Algorithm for Bose Systems with Periodic Boundary Conditions

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, which 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 by 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.

Automated summary

This article provides a detailed description of the path-integral Monte Carlo worm algorithm for exact calculations of the thermodynamics of Bose systems in the canonical ensemble. The algorithm is applicable to homogeneous phases of bulk systems with periodic boundary conditions and allows for sampling of the probability distribution function without limitations on the length of the Monte Carlo moves. By adopting a specific representation of the path coordinates, the algorithm ensures detailed balance for any update of the path configurations without selecting the periodic image of the particles involved.