SciPost Submission Page
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 |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2312.13498v2 (pdf) |
| Date submitted: | 2024-01-05 07:25 |
| Submitted by: | Song, Menghan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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.
Current status:
Reports on this Submission
Strengths
This paper has several strengths
1- Very reliable QMC study of the Entanglement Entropy, a quantity notoriously difficult to measure.
2-Very thorough, careful and important study of various states of 2D quantum matter (symmetry-broken, (2+1)d O(3) QCP, DCQP).
3-Trigger very interesting questions about possible new log corrections at the DCQP
Weaknesses
I do not see any weaknesses
Report
I first want to apologise for my late report...
In this work, the authors present very convincing QMC results for the entanglement entropy in various important quantum states of matter.
Their results are very well presented and very convincing. I have only very minor comments or suggestions that could serve either for this work or for future research.
1/ It may be fair to recall some of the past efforts made using large-S calculations that basically also brought strong justifications to Eq. (6), in particular also to extract subleading constant strip corrections. For example using square vs strip contributions in PHYSICAL REVIEW B 92, 115126 (2015) they precisely extract corner terms, a trick that could also be used by the present authors for their study.
2/ In Fig. 4(b), it seems that the area-law prefactor is the same for both DQCPs : is that true?
3/ Concerning the log correlations at the DQCPs, I like very much the interpretation in terms of the unusual finite-size scaling of the stiffness and susceptibilities that may best be written like this
S(L)= aL + \frac{n_G}{2}\ln\left[L\sqrt{\chi_\perp\rho_s}\right]+\gamma_{ord} (see Eq. 1.5 from Metliski and Grover).
From the above form, is that correct, following "Quantum criticality with two length scales" by Shao, Guo and Sandvik, that one expects the log term to be simply \frac{n_G}{2}(1-\nu/\nu')\ln L ?
If so could the authors maybe write it and comment why this correction is different between the two DQCP models?
4/ Finally do the authors expect similar unconventional corrections at a first order transition between a Néel order and a gapped state for instance?
Despite these few questions and comments I recommend this work to be published.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
1. The paper presents state-of-the-art numerical simulations of the finite-size scaling of the Rényi entropy for different quantum many-body phases.
2. Their simulations cover a broad range of cases, including deconfined quantum critical points (DQCP), which have recently been under debate in the literature.
3.Their precise numerical results allow not just the confirmation of some theoretical results, but also the identification of possible discrepancies with theoretical expectations.
4. The authors even propose some possible explanations for the size scaling of the Rényi entropy in the case of DQCP.
Weaknesses
1. The authors could comment more on some details of the QMC simulations used in this work.
2. The idea of using the "subtracted EE" was already explored in similar contexts (e.g., in New Journal of Physics 22 (1), 013044); they could have commented on this
Report
The paper by Menghan Song et al. employs recent algorithmic advances to obtain the finite-size scaling of the Renyi entropy in different paradigmatic quantum phases. In particular, their large-scale simulations provide access to universal subleading corrections to the Renyi entanglement entropy (EE).
Overall, despite the methods employed by the authors not being new, I believe their precise results for the universal corrections of the Rényi EE are relevant to the field. Specifically, their results allow for drawing comparisons with theoretical expectations from quantum field theories. For example, the numerical results for the O(3) Quantum Critical Point (QCP) indicate a much smaller constant than expected for the free boson fixed point, while in the DQCP, they observe a positive coefficient for the logarithmic correction.
Requested changes
I just have suggestions of change.
1. Include the results of the constant of constant $\gamma$ in table Table 1. The absolute value $\gamma$ increases with Lmin? Maybe the author could mention the its value for a third value of Lmin, similar to what they do for the content $s$.
2. Include some information about the QMC simulations.