之前的文章 Geometric entanglement in the Laughlin wave function 在njp审稿4个月，刚刚获得意见。开始2个审稿人，一正一负，编辑找了第三个。这第三个偏正，编辑让大修，之后算重投。

工程艰巨，前途未卜，可能放弃算了

第二个审稿人没有太明白我们的意思。一般的纠缠度度量是基于schmidt分解的，需要对系统做bipartition，但这正是这种做法对全同粒子系统不合适的原因。那个越南人在pra上被引用400次的文章，他貌似不知道。

第一个审稿人提的问题，也确实是我们没头绪的地方。

Dear Dr Zhang,

Re: "Geometric entanglement in the Laughlin wave function" by Zhang, Jiang min; Liu, Yu

Your Paper, submitted to New Journal of Physics, has now been refereed and the referee report(s) can be found below and/or attached to this message.

We regret to inform you that your Paper is not suitable for publication in New Journal of Physics in its current form. The changes requested by the referees are substantial and are too significant to warrant a revision of the article in its current form.  However, the referee(s) feel that if you rewrite the article as explained in the referee reports, including any further work recommended, it may then be suitable for reconsideration.

If you wish to rewrite your Paper, please take the referee comments fully into account and provide point-by-point responses with a full list of changes. We will treat the rewritten article as a new submission with a new article reference number and it will be peer reviewed again.  Although we will go back to the previous referees for their opinion where possible, we may also contact further referees in order to ensure that the rewritten article meets our high quality and interest criteria. If it does not, the new version of the manuscript will be rejected.

You can resubmit your revised manuscript here: *** PLEASE NOTE: This is a two-step process. After clicking on the link, you will be directed to a webpage to confirm. ***

https://mc04.manuscriptcentral.com/njp?URL_MASK=64665d98c4664fa78200c9264d

We would like to thank you for your interest in New Journal of Physics.

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On behalf of the IOP peer-review team:

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Jessica Thorn and David Murray - Associate Editors

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Dr Elena Belsole - Executive Editor

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REFEREE REPORT(S):

Referee: 1

COMMENTS TO THE AUTHOR(S)

Following the work of other authors on models with topological order, in the manuscript the authors calculate the geometric entanglement for the Laughlin wave function by numerically projecting it on the wave function given by a Slater determinant.

The problem is very interesting and deserve consideration. Also the paper is written in a clear way. However I believe that the paper should be amended before publication since, after having found deep differences with previous results,  the authors do not try to give any explanation and hence do not drive any conclusion.

In particular the authors should address he following points:

1)Some more details on numerics would be at order, in order to understand the computational effort: what is the highest value of N one could think of using? This is important since: i) with respect to other computational methods, N=9 appears to be small, ii) N=9 seems to be very far from thermodynamical limit.

2)The similarities and differences between this model and other models with topological orders (such as the one discussed in ref. [30]) are not presented. But one can wonder whether i) it is only a matter of considering a strongly correlated system; ii) particle statistics plays any role.

3)On what grounds one should expect or not to expect a linear behaviour with N?

4)can the authors try to justify why the constant term in E_G does not yield the topological entropy?

5)I find Fig. 1  quite confusing, since the negative value of E_G is plotted.

Finally, let me stress that a better explanation of what is happening in this model could be very helpful to understand the meaning of geometric entanglement. Therefore I really hope the authors will try to improve their manuscript.

Referee: 2

COMMENTS TO THE AUTHOR(S)

Dear Editor,

In the draft `Geometric entanglement in the Laughlin wave function',the authors study what they call the `geometric entanglement' of the Laughlin wave function, which describes a complicated many body system of interacting electrons.

Using an existing technique, the authors determine which Slater determinant `contributes the most', or in other words, has the largest overlap with the wave function itself. They then consider the log of this overlap, and call it the `geometric entanglement'. It is not clear to us what this quantity has to do with the entanglement properties of the many body Laughlin state, after all, no bipartition is made. So, one should just consider it as the (log of) the overlap of the most important Slater determinant with the total wave function.

The Laughlin state is a many body wave function, for which the number of Slater determinants grows exponentially in the number of particles, it is not surprising that the log of the most important Slater determinant decreases linearly with the system size. Moreover, this behavior has nothing to do with the entanglement properties of the Laughlin state. It is therefore not surprising that the attempt of the authors in linking their results to the entanglement entropy of the Laughlin state was not successful.

In conclusion, one can not access entanglement properties of a many body state by looking at a single Slater determinant, even if it is the one that contributes the most to the wave function. Therefore, this draft should not be published.

Referee: 3

COMMENTS TO THE AUTHOR(S)

In the manuscript "Geometric entanglement in the Laughlin wave function", the authors propose an efficient numerical method based on an existing approach to investigate the Laughlin many body wave function properties related to geometric entanglement.

The authors calculate the Slater determinant wave function, such that the overlap between this Slater determinant and the Laughlin many-body wavefunction is maximal. They claim that this overlap (its logarithm) is a measure of the geometric entanglement. A standard approach to the problem of entanglement utilizes bipartition or considering correlation of the specific observables (see through discussion in T. A. KAPLAN, Fluct. Noise Lett., 05, C15 (2005)). This has been thoroughly criticized by the 2nd referee.

We find that (1) the results presented in the manuscript are interesting and worthy of publication, but the present version of the manuscript does not justify the given interpretation, as criticized by the 2nd referee. (2) The authors should calculate entanglement via standard procedure and compare their result with the standard approach. If they agree, their interpretation can remain. (3) If not, the authors should rewrite their paper and provide a different interpretation of their result. They should explore the point raised by the referees and examine the state space dimension effect as the cause of the trend in the overlap (see appropriate points in 1st and 2nd referee report).

COMMENTS FROM EDITORIAL BOARD:

Associate Editor

Comments to the Author:

The paper  has been reviewed by three referees. According to their report, the paper needs major revision before publication. We urge the authors to consider all the criticism raised by the referees, and resubmit only if they feel to be able to overcome the criticisms.