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Many versus one: the disorder operator and entanglement entropy in fermionic quantum matter

by Weilun Jiang, Bin-Bin Chen, Zi Hong Liu, Junchen Rong, Fakher F. Assaad, Meng Cheng, Kai Sun, Zi Yang Meng

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Submission summary

Authors (as registered SciPost users): Fakher Assaad · Bin-Bin Chen · Meng Cheng
Submission information
Preprint Link: scipost_202306_00006v1  (pdf)
Date accepted: 2023-06-21
Date submitted: 2023-06-07 07:20
Submitted by: Chen, Bin-Bin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the $\log{L}$ scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal $L\log L$ scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provides new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

Author comments upon resubmission

Dear Editors,

Thank you for considering our manuscript, “Many versus one: the disorder operator and entanglement entropy in fermionic quantum matter”, for publication in SciPost and for providing us the reviewers’ insightful comments. We appreciate your and reviewers’ time and efforts in reviewing our work. We are grateful for the overall supportive and constructive comments from both reviewers. We believe that the changes made in response to these feedbacks have significantly improved our manuscript and we hope that it now meets the standards of the SciPost. Hopefully the revised manuscript will be accepted for publication soon.

Weilun Jiang, Bin-Bin Chen, Zi Hong Liu, Junchen Rong, Fakher F. Assaad, Meng Cheng, Kai Sun and Zi Yang Meng

List of changes

Below are the list of changes refer to the comments, these changes are also marked in red in the revised manuscript for their easy identification.
1. We list our main innovation points at the end of the Section II of key results. Besides we change the order of paragraphs in Introduction section. All of these changes are to show our original results more clearly.
2. We move the analysis of the disorder operator with well-known bosonization techniques of 1D system to the Supplemental Materials. Furthermore, we add more discussion on PM/FM phase in the 2D interacting system, according to the suggestions of the reviewers.
3. Finite temperature extension and negativity related work are discussed, with the suggested reference explicited cited.
4. Grammar and typos are carefully checked and fixed. References are updated.

Published as SciPost Phys. 15, 082 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-6-8 (Invited Report)


The authors have submitted a revised manuscript that adequately addresses all the previous concerns and weaknesses. Based on this, I strongly recommend publication without any additional revisions.

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