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

Year: 2022

Authors: Spada Gabriele; Giorgini Stefano; Pilati Sebastiano

Autors Affiliation: Dipartimento di Fisica, Universita di Trento, CNR-INO BEC Center, Trento, 38123, Italy; School of Science and Technology, Physics Division, Universita di Camerino, Camerino, 62032, Italy; INFN-Sezione di Perugia, Perugia, 06123, Italy

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, 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.


Volume: 7 (2)      Pages from: 30-1  to: 30-21

More Information: This work was supported by the Italian Ministry of University and Research under the PRIN2017 project CEnTraL 20172H2SC4. S.P. acknowledges PRACE for awarding access to the Fenix Infrastructure resources at Cineca, which are partially funded from the European Union´s Horizon 2020 research and innovation programme through the ICEI project under the grant agreement No. 800858. S.P. also acknowledges the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support.
KeyWords: path-integral; Monte Carlo; periodic boundary conditions; worm algorithm; ultracold Bose gases
DOI: 10.3390/condmat7020030