SciPost Submission Page
Extracting electronic many-body correlations from local measurements with artificial neural networks
by Faluke Aikebaier, Teemu Ojanen, Jose L. Lado
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Faluke Aikebaier · Jose Lado |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202212_00066v1 (pdf) |
| Code repository: | https://zenodo.org/record/6611506 |
| Data repository: | https://zenodo.org/record/6611506 |
| Date accepted: | 2023-02-13 |
| Date submitted: | 2022-12-23 08:35 |
| Submitted by: | Aikebaier, Faluke |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We demonstrate that by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work demonstrates that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.
Author comments upon resubmission
We are resubmitting our manuscript "Extracting electronic many-body correlations from local measurement data with artificial neural networks" for consideration in SciPost physics.
First, we would like to thank you for your consideration and for providing the opportunity to transfer our work to SciPost Physics Core. We believe that in our revised version we have addressed all the criticisms of the Referees, and therefore we hope that you reconsider our work in Scipost Physics. We are fully aware that SciPost Physics aims at publishing groundbreaking results obtained in any sub-specialization of physics, and we believe that our manuscript demonstrates exactly this.
Our manuscript was reviewed by two referees. In both of the referees' reports, our work is considered interesting and our article is clear. Referee 2 recommended our manuscript for publication in SciPost physics if we addressed the points mentioned. Referee 1 mentioned several criticisms, concluding that he/she was not convinced of the suitability of our manuscript in SciPost Physics. We believe that the criticism of Referee 1 arose due to a minor misunderstanding of specific points of our manuscript. In our revised manuscript and response we have clarified all those points in detail, and we, therefore, hope that the Referee reconsiders his/her position.
In our work, we put forward the first concrete protocol which would allow experimental extraction of the Fock-space entanglement and electronic many-body correlations. Our work addresses a critical problem in quantum materials, of major interest to the experimental and theoretical research community in quantum materials.
We hope that, given our response and all the points above, you reconsider our manuscript as suitable for publication in SciPost Physics.
Yours sincerely,
Faluke Aikebaier, Teemu Ojanen and Jose Lado
List of changes
- We have added some description about supervised learning with neural network algorithms in the introduction and added related citations, including J. Phys. Soc. Jpn. 86, 093001 (2017), J. Phys. Soc. Jpn. 88, 065001 (2019)
- We have added a discussion about the finite-size dependence of the correlation entropy and added a figure in appendix 8.1
- We have added a discussion about the potential extension of our work to 2D systems in the Method section
- We have added more discussion about the noise and added figures in appendix 8.2
- We have added new references
Published as SciPost Phys. Core 6, 030 (2023)
Reports on this Submission
Report
I thank the authors for their responses to my questions, and for the corresponding changes that were made to the manuscript.
The main point of the article has not changed: the authors propose a way to estimate the correlation entropy of a system of interacting fermions from a reduced set of correlators, through the use of a neural network algorithm. Predictions can only be made for experimental devices that simulate models that can be solved numerically to train the neural network, which reduces the scope of this work, and does not open the door to new results. Therefore, I still feel that this work is not suitable for publication in this SciPost Physics.
However, the work is interesting and well presented, and with this improved version of the manuscript, I would recommend publication in SciPost Physics Core instead.
Report #1 by Izak Snyman (Referee 1) on 2023-1-5 (Invited Report)
- Cite as: Izak Snyman, Report on arXiv:scipost_202212_00066v1, delivered 2023-01-05, doi: 10.21468/SciPost.Report.6458
Report
I thank the authors for their careful responses to the queries I had regarding the original manuscript. I have considered the responses carefully, and have formed the following opinion.
The authors aim for their work to pave the way for experimentalists to extract the correlation entropy of interacting fermion systems from a few single-particle measurements. However, the authors' supervised learning method only applies to systems that can be solved numerically, so that training data can be generated. Only very recently have prospects started opening up for faithful realisations of the idealised models that theorists can "solve" numerically. This is the nascent field of quantum simulation. Now, if I have a quantum simulator of a model that can be solved numerically, and I want to know the entanglement entropy, I would simply perform the measurements required to confirm that the simulator is faithful, and then calculate the entropy. The authors' method provides no advantage, since it does not work if the simulator is not faithful.
The actual experimental challenge is to estimate the correlation entropy when we do not know how to model the system, or when the only solvable models are idealised representation of a real experiment, that (hopefully) still belongs to the same "universality class". The authors results provide interesting food for though for researchers who want to tackle this problem: perhaps there is some robust link , that is not very model-specific, between the handful of correlators that the authors compute, and the correlation entropy. Perhaps an unsupervised learning algorithm can uncover it. I therefore find that the manuscript meets the acceptance criteria of SciPost Physics Core as it "[a]ddress[es] an important (set of) problem(s) in the field using appropriate methods with an above-the-norm degree of originality" and "[d]etail[s] one or more new research results significantly advancing current knowledge and understanding of the field". However, given the obstacles that lie between the authors results and a breakthrough or a new pathway, the work does not meet the requirements for publication in SciPost Physics proper.