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Efficient and scalable path integral Monte Carlo simulations with worm-type updates for Bose-Hubbard and XXZ models

Nicolas Sadoune, Lode Pollet

SciPost Phys. Codebases 9 (2022) · published 29 November 2022

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DOI Type
10.21468/SciPostPhysCodeb.9 Article
10.21468/SciPostPhysCodeb.9-r1.0 Codebase release

Abstract

We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.

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