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Symmetry decomposition of negativity of massless free fermions

by Sara Murciano, Riccarda Bonsignori, and Pasquale Calabrese

Submission summary

As Contributors: Sara Murciano
Preprint link: scipost_202103_00002v2
Date accepted: 2021-05-10
Date submitted: 2021-04-20 13:49
Submitted by: Murciano, Sara
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.

Published as SciPost Phys. 10, 111 (2021)

Author comments upon resubmission

We are submitting a revised version of the manuscript "Symmetry decomposition of negativity of massless free fermions".
We would like to thank the editors for their work and the referees for
their useful comments and suggestions.

List of changes

- We modified all typos/misleading/wrong expressions.
- We commented on the validity of our results for interacting models.
- We tried to clarify the basis dependence of the charge operator.
- We clarified the confusing notations in Appendix C.

Reports on this Submission

Anonymous Report 2 on 2021-5-5 (Invited Report)


The authors have addressed all my concerns, I recommend publication.

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

Anonymous Report 1 on 2021-4-23 (Invited Report)


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

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

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