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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 | |
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| Preprint Link: | https://arxiv.org/abs/2204.12262v2 (pdf) |
| Code repository: | https://github.com/LodePollet/worm |
| Date submitted: | Sept. 16, 2022, 6:56 a.m. |
| Submitted by: | Lode Pollet |
| Submitted to: | SciPost Physics Codebases |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
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.
Author comments upon resubmission
List of changes
- 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.
- Added two tutorials to the repo
- Added a second way to construct lattices based on XML files. Forked from the library provided by S. Todo.
Current status:
Reports on this Submission
Strengths
I am happy with the responses and changes, except for very minor requested additions, see below.
Weaknesses
Report
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.