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

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.

v1: 18 pages, 6 figures. v2: Fixed typo in eq.(30) and (31), minor changes, matches published version

References in corpus (7)

• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas
• The fate of vacancy-induced supersolidity in 4He
• Phase diagram of 4He adsorbed on graphite
• Quantum statistics and the momentum distribution of liquid para-hydrogen
• Phases of dipolar bosons in a bilayer geometry
• Berezinskii-Kosterlitz-Thouless Transition in Two-Dimensional Dipolar Stripes