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Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension

by Shachar Fraenkel and Moshe Goldstein

Submission summary

As Contributors: Shachar Fraenkel · Moshe Goldstein
Preprint link: scipost_202105_00012v2
Date accepted: 2021-09-22
Date submitted: 2021-08-29 21:19
Submitted by: Fraenkel, Shachar
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics. However, exact analytical results remain scarce, especially for systems out of equilibrium. In this work we examine a paradigmatic one-dimensional fermionic system that consists of a uniform tight-binding chain with an arbitrary scattering region near its center, which is subject to a DC bias voltage at zero temperature. The system is thus held in a current-carrying nonequilibrium steady state, which can nevertheless be described by a pure quantum state. Using a generalization of the Fisher-Hartwig conjecture, we present an exact calculation of the bipartite entanglement entropy of a subsystem with its complement, and show that the scaling of entanglement with the length of the subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term. The linear term is related to imperfect transmission due to scattering, and provides a generalization of the Levitov-Lesovik full counting statistics formula. The logarithmic term arises from the Fermi discontinuities in the distribution function. Our analysis also produces an exact expression for the particle-number-resolved entanglement. We find that although to leading order entanglement equipartition applies, the first term breaking it grows with the size of the subsystem, a novel behavior not observed in previously studied systems. We apply our general results to a concrete model of a tight-binding chain with a single impurity site, and show that the analytical expressions are in good agreement with numerical calculations. The analytical results are further generalized to accommodate the case of multiple scattering regions.

Published as SciPost Phys. 11, 085 (2021)

Author comments upon resubmission

Dear Editor,

Attached is a new version of our manuscript following the requested revision. We would like to thank the Referees for reading our manuscript thoroughly, and for their comments which gave us the opportunity to clarify some important points within the text. We are very glad that both Referees have recommended our manuscript for publication in SciPost Physics. We detail in the response to each referee the modifications we have applied following each specific comment. In addition, we have used the opportunity to correct some typos and add a few additional references. The parts of the manuscript that were modified in light of these comments by the Referees are marked in red in the new manuscript. We believe that this revised version is now ready for publication.

Shachar Fraenkel and Moshe Goldstein

List of changes

The changes to our manuscript are detailed in our responses to the Referees.

Reports on this Submission

Anonymous Report 2 on 2021-9-12 (Contributed Report)


The authors answered all the points raised in the first round of review.

I thank them for their clear reply and raccomend the paper for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2021-8-30 (Invited Report)


I am happy with the changes/clarifications made by the authors and I recommend this article for publication.

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

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