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Gaussian state approximation of quantum many-body scars
by Wouter Buijsman, Yevgeny Bar Lev
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Submission summary
| Authors (as registered SciPost users): | Yevgeny Bar Lev · Wouter Buijsman |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202307_00041v3 (pdf) |
| Date submitted: | 2024-07-01 19:13 |
| Submitted by: | Buijsman, Wouter |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.
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Author comments upon resubmission
We are grateful to the Referee for providing us with useful comments, remarks and suggestions. We have implemented all requested changes in the revised version. Please find below our reply to each of the points in the report. Hereby, we would like to resubmit our manuscript to SciPost Physics.
Yours sincerely,
Wouter Buijsman
Yevgeny Bar Lev
List of changes
- Changed from open to periodic boundary conditions.
- Clarified on the implementation of the Jordan-Wigner transformation.
- Expanded the discussion on possible properties of parent Hamiltonians.
- Commented on the quality of the approximations in view of previous results.
- Implemented minor corrections on issues pointed out in the report.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2024-7-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202307_00041v3, delivered 2024-07-15, doi: 10.21468/SciPost.Report.9402
Strengths
As previously described
Weaknesses
As previously described
Report
Our questions have been addressed.
Now the authors have switched to analyzing the model with periodic boundary conditions and seem to obtain cleaner structures for their wavefunctions.
The point (site 1) where the Jordan Wigner transformation is rooted breaks translational invariance of the resulting fermionic Hamiltonian. This is (at least) reflected in sign changes of the elements of A and B matrices as the root is crossed. This should be discussed.
The resulting A and B matrices are surprisingly invariant upon translation by 2 sites. However, the eigenstates of the original Hamiltonian are obviously translation invariant (by one site). To what extent are the quadratic trial wavefunctions close to being 1-site translation invariant, even though they do not have explicitly this structure? This should be commented on.
Now the procedure and approach are explained clearly, such that a reader can appreciate what the content of the work is.
I have commented previously on the limited scope of the approach. This has remained unchanged and the work just barely makes the bar of some of the criteria for SciPost. However, the work can be published.
Requested changes
1. The degree to which trial scar states are approximately translationally invariant should be discussed, as well as the reason, why translation invariance is not enforced by applying a symmetrizer.
2. The effect of the choice of the root for the JW transform should be mentioned, as it is indeed reflected in the structure of A and B.
Recommendation
Ask for minor revision
Author: Wouter Buijsman on 2024-07-31 [id 4668]
(in reply to Report 1 on 2024-07-16)We thank the Referee for their constructive report and positive attitude towards our manuscript. Please find our reply to both of the points below.
The referee writes:
Our response:
The remark made by the Referee is correct, and is in agreement with what we observe in the color plots of matrices $A$ and $B$ as shown in Fig. 3. We have added this remark in the revised version.
The referee writes:
Our response:
Let us remind the Referee that we focus on the overlap of symmetrized Gaussian states [defined in Eq. (7)] with quantum many-body scars. The symmetrization of a state invariant by translation over two sites leads to a state translationally invariant by one site. With this in mind, it does not come as a surprise that the resulting $A$ and $B$ matrices are almost invariant upon translation by two sites. If the overlap between a (symmetrized) trial wavefunction and a quantum many-body scar is close to unity, the trial wavefunction and the quantum many-body scar are nearly identical. Then, the trial wavefunction is almost translationally invariant. We have elaborated on both of these points in the revised version.