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Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

by Tommaso Micallo, Vittorio Vitale, Marcello Dalmonte, Pierre Fromholz

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Marcello Dalmonte · Pierre Fromholz · Vittorio Vitale
Submission information
Preprint Link:  (pdf)
Code repository:
Data repository:
Date accepted: 2020-11-17
Date submitted: 2020-11-02 15:39
Submitted by: Fromholz, Pierre
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational, Phenomenological


We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants.

Author comments upon resubmission

Dear Editor-in-Charge,

We thank you for both your reply and your consideration of our manuscript.
As recommended, we revised the text of the manuscript. We thank both Referees for their comments. Please find our reply to the Referees’
reports and the list of subsequent changes from the previous version of the manuscript to the resubmitted version. Please also find the
resubmitted version of our manuscript.
We hope both you and the referees will find the new version satisfactory.

Yours sincerely,
The authors.

List of changes

— To answer the main concerns of the two Referees, we significantly rewrote
the introduction and the discussion part of the conclusion, and
added two subsections (5.1 and 7.1). We list more specific changes
— We modified the end of the abstract.
— We modified (added) the titles for section 3, 4, 4.2, 5, 5.1, 5.2, 6, 7.1
— We stress more our main results in the introduction and stressed the
differences with Ref.31 (ex Ref.28) (the first main point of both Referees)
and added Ref.32 and 39 to do so.
— We added Ref. 9-11 (point 3 of the second Referee), 36-37 (point 1.2
of the second Referee).
— We clarified the second paragraph of 2.1 (point 5 of the second Referee).
— We removed a word in the fourth paragraph of 2.1 (point 6 of the
second Referee).
— We corrected a typo in the same paragraph and modified the sentence
accordingly. One reference (ex. Ref 47) was replaced in the process by
— We added footnote 4 with Ref. 48 (point 1.3 of the second Referee, also
cited later).
— We slightly rephrased the first sentence of 2.3.
— We added two sentences at the end of 2.3 (point 1.1 of the second
— We slightly rephrased the first paragraph of 2.4 and corrected a typo
in the second.
— We slightly rephrased the first paragraph of 3
— We added a sentence in the second paragraph of 3 with Ref.59 (point
7 of the second Referee).
— We slightly rephrased the third paragraph of 3
— We added sentences to the first paragraph of 4.1 (point 1.3 of the
second Referee).
— We added section 5.1, added Ref. 64-67, and reformulated the start
of Sec.5 accordingly (point 2 of the second Referee, and also partially
answer the first main concern of both Referees and the second main
concern of the second Referee).
— We added Figs. 4c and d) and added the relevant caption in 5.2 (point
8 of the second Referee). We modified 5.2 to take these figures into
— We added a sentence and Ref. 69 to 5.2 (point 1.4 of the second Referee).
— We corrected a typo on the number of realization mentioned in the
caption of Fig.5.
— We added Sec. 7.1 and modified the discussions and conclusions accordingly
(all main concerns of both Referee). We added the relevant
Ref.77 and 78.
— We now mention where to find the code and data used in the text with

Published as SciPost Phys. Core 3, 012 (2020)

Reports on this Submission

Anonymous Report 1 on 2020-11-12 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2006.15026v2, delivered 2020-11-12, doi: 10.21468/SciPost.Report.2183


I thank the authors for the very clear and thorough reply. I think that that all of my questions about the content have been adequately addressed, and the current version also makes clearer what the novelty and achievements are of this particular work. The only question left is whether this is sufficient to satisfy the publication criteria of SciPost Physics Core, and I am happy to say that the authors have also convinced me of this with the clearer presentation of their results (as summarised in their response). I recommend publication.

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