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Scaling of disorder operator at deconfined quantum criticality
by Yan-Cheng Wang, Nvsen Ma, Meng Cheng, Zi Yang Meng
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We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.
Author comments upon resubmission
Both referees also give valuable suggestions for the improvement of our presentation, which have been incorporated in the main text. We have also added new sections in the Supplemental Materials to address the comments from the referees. With these changes, the narrative of our manuscript has been greatly improved and we really appreciate the help from both respected referees.
List of changes
1. Responding to the comments of referees, we added Fig.4, Fig.7(b) Fig.9(b) and modified Fig.9(c).
2. Turned the SM into regular appendices.
3. Corrected typos and updated references.
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2106.01380v3, delivered 2022-07-05, doi: 10.21468/SciPost.Report.5306
I thank the authors for considering the suggested changes to their manuscript. However, regarding two of my previous points, I still request changes:
With regards to my request 2, I don't consider the new Fig. 4 to be useful to understand the quoted values of chi (btw: is this chi/DOF?). The authors can improve on this by simply plotting the relative differences so that one can indeed see the deviations between the data and the red fit line on the scale of the error bars.
With regards to my request 6, the authors have not responded appropriately: I asked them to show in the former Fig. 5 (now Fig. 9) the data for a naive measurement, i.e., without considering the even/odd character. Please include such a measurement as well. Panel 10c is not related to this point.
- Cite as: Anonymous, Report on arXiv:2106.01380v3, delivered 2022-07-05, doi: 10.21468/SciPost.Report.5335
I thank the authors for their clarifications and efforts to improve the data analysis.
I still think the discussion of error bars in the main text is too sparse. Results for s(theta) are quoted in the main text with error bars of the order of 2%. But the large deviations between curves in Figure 7 c and 9 c suggest that quantifying the error bar is a nontrivial issue, and it deserves discussion in the main text.
At present, the authors argue that the preferred protocol is safe because it agrees a known result in the J1-J2 case. But in the absence of any direct extraction of an error bar to compare between protocols, (a) how do we know this agreement is not a coincidence, (b) how do we know that the preferred protocol will be safe also in J-Q3 case?
Can the accuracy for each protocol be quantified in some way from the data? The authors give a numerical error bar for one protocol. How is it obtained, and can be it be compared between protocols to give direct comparison?
If the authors cannot directly quantify the error bar then at least there should be some discussion in the main text of the fact that there are nontrivial discrepancies between different protocols.
Apart from this the other issues have been addressed, so when the authors have resolved the above to their satisfaction the paper can be published.