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Efficient and scalable Path Integral Monte Carlo Simulations with worm-type updates for Bose-Hubbard and XXZ models

by Nicolas Sadoune, Lode Pollet

This is not the latest submitted version.

Submission summary

Authors (as registered SciPost users): Lode Pollet
Submission information
Preprint Link:  (pdf)
Code repository:
Date submitted: 2022-09-16 06:56
Submitted by: Pollet, Lode
Submitted to: SciPost Physics Codebases
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
Approach: Computational


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.

Author comments upon resubmission

We answered to the Referee Reports separately. All information is provided in our Comments to their Reports.

List of changes

1. Changed wording throughout the text in response to the Referee Reports; in particular, we replaced Fig 8 with a new figure showing the average kinetic energy per site as a function of linear system size for a critical system.
2. Added two tutorials to the repo
3. Added a second way to construct lattices based on XML files. Forked from the library provided by S. Todo.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 3 on 2022-9-28 (Invited Report)


The authors have responded appropriately to the requests. I have no further requests and recommend the revised version for publication.

  • validity: -
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  • originality: -
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  • grammar: -

Anonymous Report 2 on 2022-9-27 (Invited Report)


The authors have addressed all of my concerns. I recommend publication as is.

  • validity: -
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Anonymous Report 1 on 2022-9-20 (Invited Report)


Strengths as mentioned before. Greatly appreciated.
I am happy with the responses and changes, except for very minor requested additions, see below.


See requested changes.



Requested changes

Very minor.
1) In Figs 5-7, the unit for the autocorrelation time, e.g. "tau_W^2=55" apparently still needs to be specified (updates?).
2) Fig. 8: It would be helpful to roughly know the proportionality factor, or alternatively the actual memory consumption for some system size.
3) Updates per second in the text: hardware should again be specified, similar to v1.

  • validity: top
  • significance: top
  • originality: -
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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