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Robust multipartite entanglement in dirty topological wires

by Luca Pezze' and Luca Lepori

Submission summary

As Contributors: Luca Pezze
Preprint link: scipost_202204_00008v1
Date submitted: 2022-04-05 15:19
Submitted by: Pezze, Luca
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Identifying and characterizing quantum phases of matter in the presence of long range correlations and/or spatial disorder is, generally, a challenging and relevant task. Here, we study a generalization of the Kiteav chain with variable-range pairing and different site-dependence of the chemical potential, addressing commensurable and incommensurable modulations as well as Anderson disorder. In particular, we analyze multipartite entanglement (ME) in the ground state of the dirty topological wires by studying the scaling of the quantum Fisher information (QFI) with the system's size. For nearest-neighbour pairing the Heisenberg scaling of the QFI is found in one-to-one correspondence with topological phases hosting Majorana modes. For finite-range pairing, we recognize long-range phases by the super-extensive scaling of the QFI and characterize complex lobe-structured phase diagrams. Overall, we observe that ME is robust against finite strengths of spatial inhomogeneity. This work contributes to establish ME as a central quantity to study intriguing aspects of topological systems.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2022-6-1 (Invited Report)


1 Transparent presentation
2 Contextualization


1 No original results
2 Method (multipartite entanglement) might not readily generalize to other more complicated topological phases


To publish or not publish this manuscript in SciPost relies on the assessment to which extent truly new results are a prerequisite for publication. I cannot exclude the possibility that multipartite entanglement, as the authors propose, could become highly relevant in the future - this would speak in favor of publication. At today's stage, however, the amount of original results obtained through multipartite entanglement for the Kitaev chain, as communicated in the manuscript, is very limited. In total, I wish to leave this part of the assessment to the editor-in-charge.

Requested changes

Maybe the authors would like to consider exploring more aspects of entanglement in the Kitaev chain.
1. For instance, the Kitaev chain relates to the Ising model via Jordan Wigner transformation, which is sui generis non-local: (for a later discussion see e.g. How does multipartite entanglement depend on the basis in which the Schmidt decomposition is performed?
2. The authors talk about parametric variations of the chemical potential mu in their article. Could they also just simulate the evolution of entanglement under braiding which would be performed through the variation of mu? (see e.g.

  • validity: good
  • significance: ok
  • originality: ok
  • clarity: high
  • formatting: perfect
  • grammar: good

Anonymous Report 1 on 2022-5-26 (Invited Report)


The paper gives a solid analysis of a long-range free fermion model in the presence of disorder through the analysis of quantum Fisher information (QFI). The study takes into account various types of disorder and different ranges of the hopping. The authors connect the properties of the QFI with the underlying topology of the free fermion model.


In my opinion the paper points out that the QFI can detect features of the models. It avoids however in trying to go deeper trying to understand what is the reason behind it. QFI, after all, is related correlation functions. It is therefore natural to imagine that this is the reason why the presence of edge modes may contribute. If this is the only reason, I would feel that the observations made on the QFI are a direct consequences of what we know already on the model studied.


The paper is a careful study of a long-range Kitaev chain in the presence of disorder. The model has been extensively studied in the past. The new ingredient is the analysis of the QFI. While the technical part is described very well, the consequences are not discussed. It is not clear what we learn on the model or on QFI from this paper.

Requested changes

The authors should revise considerably the discussion explaining the importance/novelty of their results.

  • validity: high
  • significance: ok
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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