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Extensive long-range entanglement in a nonequilibrium steady state

by Shachar Fraenkel, Moshe Goldstein

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Submission summary

Authors (as registered SciPost users): Shachar Fraenkel
Submission information
Preprint Link: scipost_202305_00038v2  (pdf)
Date accepted: 2023-08-17
Date submitted: 2023-08-10 11:24
Submitted by: Fraenkel, Shachar
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of noninteracting fermions at zero temperature in the presence of a scatterer. We show that disjoint intervals located on opposite sides of the scatterer, and within similar distances from it, maintain volume-law entanglement regardless of their separation, as measured by their fermionic negativity and coherent information. The mutual information of the intervals, which quantifies the total correlations between them, follows a similar scaling. Interestingly, this scaling entails in particular that if the position of one of the intervals is kept fixed, then the correlation measures depend non-monotonically on the distance between the intervals. By deriving exact expressions for the extensive terms of these quantities, we prove their simple functional dependence on the scattering probabilities, and demonstrate that the strong long-range entanglement is generated by the coherence between the transmitted and reflected parts of propagating particles within the bias-voltage window. The generality and simplicity of the model suggest that this behavior should characterize a large class of nonequilibrium steady states.

Author comments upon resubmission

Dear Editor,

We hereby submit the requested revised version of our manuscript. We would like to thank the Referees for their valuable comments on our manuscript, and for recommending it for publication in SciPost Physics. In each of our replies to the Referees we detail the specific changes that we have made following their comments. These modifications are also marked in red in the revised version. With this, we now believe that our manuscript is ready for publication.

Shachar Fraenkel and Moshe Goldstein

List of changes

- Short remarks added to Section 2, Section 5 and Appendix A (all marked in red).
- Typo fixed in Eq. (B7).
- A data point in panel (f) of Fig. 5 that was originally hidden has been enlarged to improve its visibility.

Published as SciPost Phys. 15, 134 (2023)

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