# Scaling of disorder operator at deconfined quantum criticality

### Submission summary

 Authors (as Contributors): Meng Cheng
Submission information
Date accepted: 2022-08-25
Date submitted: 2022-08-03 15:56
Submitted by: Cheng, Meng
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
Approaches: Theoretical, Computational

### Abstract

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.

Published as SciPost Phys. 13, 123 (2022)

### List of changes

Responding to the comment of referee 1, we have updatd Fig.4 and Fig.9 in the revised manuscript.

Responding to the comment of referee 2, we added a sentence in the revised manuscript to point out that the quantification of the error bar in $s(\theta)$ is certainly a nontrivial issue.

### Submission & Refereeing History

Resubmission scipost_202208_00008v1 on 3 August 2022
Resubmission 2106.01380v3 on 20 June 2022
Submission 2106.01380v2 on 1 January 2022

## Reports on this Submission

### Report

I thank the authors for implementing the requested changes.
For finalizing the paper, the authors should
(i) correct the typo " chis-quare" in the caption of Fig. 4, and
(ii) include errors bars in Fig. 4(b).

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

### Author:  Meng Cheng  on 2022-08-17  [id 2737]

(in reply to Report 2 on 2022-08-09)

We thank the referee for his/her comments. We have corrected the typo " chis-quare" in the caption of Fig. 4 in the revised manuscript.

Regarding errors bars in Fig. 4(b), since the fitting deviations $\Delta(l)$ is the difference between the fitting curves and the raw data of the disorder operator, they are an auxiliary quantities to show the quality of the fittings. Their errorbars entirely come from those of the raw data of the disorder operators as shown in Fig.4 (a). Therefore, we do not see any reason to add error bars for $\Delta(l)$ and keep the Fig.4 (b) as is.

### Report

Although the authors have not changed the analysis of error bars, they have at least flagged the issue in the text. Therefore I am happy for the paper to proceed to publication.

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