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Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere
by Johannes S. Hofmann, Florian Goth, Wei Zhu, Yin-Chen He, Emilie Huffman
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Johannes Stephan Hofmann · Emilie Huffman |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202401_00004v2 (pdf) |
| Date accepted: | 2024-04-25 |
| Date submitted: | 2024-04-09 02:00 |
| Submitted by: | Huffman, Emilie |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional $SU(2)$ layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.
Author comments upon resubmission
We thank you for considering our manuscript for publication in SciPost and for soliciting reports
from these referees. We have responded to each referee report and resubmitted a revised manuscript. With these changes and our responses below, we hope our manuscript is suitable for publication in SciPost.
Best Regards,
Authors
List of changes
- added a discussion of the N^4 scaling under equation 16 in the QMC simulations section of Results
- added a couple of sentences above equation (3) to clarify the Landau projection
- added the definition of the chi^2 to the paper, see new Eq. (20)
- added a more detailed discussion of the guiding design principle for the additional flavor in the last paragraph of Sec. 2.3
- added more discussion of future directions in the conclusion
- added an "int" subscript to equations (8) and (13)
Published as SciPost Phys. Core 7, 028 (2024)
Reports on this Submission
Report
The revised manuscript has successfully addressed my concerns related to computational complexity and parameter fine-tuning. I recommend it for publication as it currently stands.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
I would like to thank the authors for carefully answering my comments and for implementing them into the text. The manuscript can be published as it is.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 4) on 2024-4-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202401_00004v2, delivered 2024-04-11, doi: 10.21468/SciPost.Report.8862
Report
In response to my earlier report, the authors have responded to my comments and revised their manuscript accordingly. In particular, they have dispelled my doubts about the suitability concerning SciPost's criteria of acceptance by their clarifications. It's a good paper with a clear scope, interesting new results, and a nice perspective for future applications.
I also find their answers to my other comments persuasive and I therefore recommend publication of the manuscript in SciPost, now.
Recommendation
Publish (meets expectations and criteria for this Journal)