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Local Operator Entanglement in Spin Chains
by Eric Mascot, Masahiro Nozaki, Masaki Tezuka
This Submission thread is now published as
|Authors (as registered SciPost users):||Eric Mascot|
|Preprint Link:||https://arxiv.org/abs/2012.14609v5 (pdf)|
|Date submitted:||2023-08-28 04:03|
|Submitted by:||Mascot, Eric|
|Submitted to:||SciPost Physics Core|
Understanding how and whether local perturbations can affect the entire quantum system is a fundamental step in understanding non-equilibrium phenomena such as thermalization. This knowledge of non-equilibrium phenomena is applicable for quantum computation, as many quantum computers employ non-equilibrium processes for computations. In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators in the one-dimensional Ising model with magnetic field and the disordered Heisenberg model to study the properties of quantum circuits. In the Ising model, the early-time evolution qualitatively follows an effective light cone picture, and the late-time value is well described by Page's value for a random pure state. In the Heisenberg model with strong disorder, we find that many-body localization prevents the information from propagating and being delocalized. We also find an effective Ising Hamiltonian that describes the time evolution of bi- and tripartite operator mutual information for the Heisenberg model in the large disorder regime.
Published as SciPost Phys. Core 6, 070 (2023)
Author comments upon resubmission
I am writing to resubmit the revised version of our manuscript titled "Local Operator Entanglement in Spin Chains”. We are grateful for the thoughtful feedback provided by the referees, and we believe that the revisions we have made address the issues raised comprehensively.
We have carefully revised the manuscript according to the reviewer's feedback, and we have also made additional improvements to enhance the clarity, analysis, and overall contribution of the work. Specifically, we have made the following changes:
We have restructured the manuscript to focus on the “full overlap” configuration and moved other configurations to the appendix.
We have included additional analysis and discussion.
We have carefully proofread the manuscript to eliminate any grammatical errors or typographical mistakes.
We believe that these revisions align the manuscript much more closely with the scope and standards of SciPost Physics Core, and we are confident that the updated version represents a substantial contribution to the field. We appreciate the opportunity to resubmit our work to SciPost Physics Core and are hopeful for a positive outcome.
Sincerely, Eric Mascot Masahiro Nozaki Masaki Tezuka
List of changes
- Revised the first few sentences of the abstract
- Revised the introduction to provide clear motivation and to better articulate the results
- Provided additional analysis of the data
- Improved the description of thermalization
- Improved the description of OTOC
- Clarified "robust against noise" for the MBL phase
- Corrected operators with maximal entanglement structure
- Added a discussion of EPR pairs in a subsystem as an interpretation of BOMI and TOMI
- Added a discussion of factorization of the density matrix as an interpretation of late-time BOMI
- Moved "partial overlap" and "disjoint" configurations to the appendix
- Added a discussion on the effective model for large disorder
- Many minor corrections
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2012.14609v5, delivered 2023-09-07, doi: 10.21468/SciPost.Report.7778
The authors have made efforts to address the comments. The essential structure of the paper remains the same and still feels a little unbalanced, with more qualitative discussion and general review (e.g. of MBL) than may be necessary (although the authors have made some effort to lighten the manuscript by taking some of the results out of the main text). It remains true that many of the take-aways from the numerical results are rather qualitative, and it is not clear to me that they go beyond previous theoretical analysis such as the reference by Kudler-Flam et al. Nevertheless the numerical results may be a reference point for future works. The background material may also be useful for some readers. On these bases the paper may now be publishable in Core.