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Symmetry decomposition of negativity of massless free fermions
by Sara Murciano, Riccarda Bonsignori, and Pasquale Calabrese
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sara Murciano |
| Submission information | |
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| Preprint Link: | scipost_202103_00002v2 (pdf) |
| Date accepted: | 2021-05-10 |
| Date submitted: | 2021-04-20 13:49 |
| Submitted by: | Murciano, Sara |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Author comments upon resubmission
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.
Published as SciPost Phys. 10, 111 (2021)