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Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
by Youenn Le Gal, Xhek Turkeshi, Marco Schirò
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Submission summary
| Authors (as registered SciPost users): | Youenn Le Gal · Marco Schirò · Xhek Turkeshi |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2210.11937v1 (pdf) |
| Date submitted: | 2022-10-28 11:43 |
| Submitted by: | Le Gal, Youenn |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider the dynamics of the non-Hermitian Su-Schrieffer-Heeger model arising as the no-click limit of a continuously monitored free fermion chain where particles and holes are measured on two sublattices. The model has $\mathcal{PT}$-symmetry, which we show to spontaneously break as a function of the strength of measurement backaction, resulting in a spectral transition where quasiparticles acquire a finite lifetime in patches of the Brillouin zone. We compute the entanglement entropy's dynamics in the thermodynamic limit and demonstrate an entanglement transition between volume-law and area-law scaling, which we characterize analytically. Interestingly we show that the entanglement transition and the $\mathcal{PT}$-symmetry breaking do not coincide, the former occurring when the entire decay spectrum of the quasiparticle becomes gapped.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-12-20 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2210.11937v1, delivered 2022-12-20, doi: 10.21468/SciPost.Report.6274
Strengths
1 . The paper demonstrates that a volume-to-area law transition in the entanglement entropy exists in a certain free fermionic system subject to a continuous monitoring via exact computations
2. It also connects the transition with a PT symmetry breaking that accompanies gap-opening.
3. Analytic results are verified by numerics.
Weaknesses
Discussions are limited to the free model (SSH model).
Report
The present article studies the entanglement dynamics in a non-Hermitian free fermionic system, which arises as the particular limit of a monitored version of it. The main finding in this paper is that the volume-to-area law transition of the entanglement entropy is triggered by a PT-symmetry breaking that leads to a gap. Interestingly, such transition is prevented for another spectral transition that simply generates gapless modes with the imaginary part. As far as I know, these different behaviours of the entanglement transition depending on the nature of PT-symmetry breaking hasn't known, and deserves further investigations. I recommend publication for this article, but I have a few suggestions which authors can choose to address.
Requested changes
1. It is not entirely clear to me why it is interesting to deal with the SSH model. It would be nice to have a brief comment to motivate the choice of this model. In particular, is there any aspect of this model that makes it somewhat different from other free fermionic systems, e.g. the Kitaev chain?
2. In the paper it is explained as to what kind of PT-symmetry breaking points induce a volume-to-area law transition at the level of spectrum, but it would be interesting to understand what the difference of these points mean in terms of quantum jumps.
3. There is a typo in the second paragraph of p.11 ("Furthermore tt"... should be replaced by "Furthermore it"...)
Strengths
see attachment
Weaknesses
see attachment
Report
See attachment