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Extracting subleading corrections in entanglement entropy at quantum phase transitions
by Menghan Song, Jiarui Zhao, Zi Yang Meng, Cenke Xu, Meng Cheng
Submission summary
| Authors (as registered SciPost users): | Meng Cheng · Menghan Song · Jiarui Zhao |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00042v1 (pdf) |
| Date accepted: | 2024-06-10 |
| Date submitted: | 2024-05-27 09:43 |
| Submitted by: | Song, Menghan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We systematically investigate the finite size scaling behavior of the R\'enyi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity ``subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that $\mathbf{(1)}$ for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; $\mathbf{(2)}$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; $\mathbf{(3)}$ for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.
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Author comments upon resubmission
Thank you very much for the editorial assessments and referee reports of our paper.
We are very happy to read the constructive comments from the two referees and have carefully considered each suggestion for improving our manuscript.
Our point-to-point responses to the referees' comments are presented below. We hope that our replies and responses are persuasive enough for you and the referees to consider our article for publication in your respected journal.
Thank you in advance for your kind consideration.
Yours sincerely,
Menghan Song, Jiarui Zhao, Zi Yang Meng, Cenke Xu, Meng Cheng
List of changes
List of changes in the revised manuscript
1. In response to referee A's comments, we have included the pertinent reference in our revised manuscript and added a table listing the fitted constant $\gamma$ of the $O(3)$ QCP for a smooth cut.
2. In response to referee A's suggestions, we have incorporated a paragraph that briefly explains the quantum Monte Carlo algorithms used to measure the second-order R\'enyi entanglement entropy.
3. In response to referee B's comments, we have incorporated the relevant reference in our revised manuscript.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)