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Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

by Simone Tibaldi, Giuseppe Magnifico, Davide Vodola, Elisa Ercolessi

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Submission summary

Authors (as registered SciPost users): Giuseppe Magnifico · Simone Tibaldi · Davide Vodola
Submission information
Preprint Link: scipost_202202_00047v2  (pdf)
Date submitted: 2022-08-01 19:19
Submitted by: Vodola, Davide
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approach: Theoretical


The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g.~to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

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Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2022-10-13 (Invited Report)


I thank the authors for the answers to my comments and for the nice revision of the manuscript. Given the nice results for the t-SNE approach in the reply to my questions, I recommend adding a small subsection discussing the t-SNE results for the non-interacting and interacting cases. It would be particularly interesting to see whether the two clusters for phase 0 correspond to TRI- and TRI+.

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Author:  Davide Vodola  on 2022-11-18  [id 3043]

(in reply to Report 2 on 2022-10-13)

We thank the Referee for their comments. We are very glad they appreciated the changes we made on the manuscript and we would like to thank them for giving us a chance to improve it. We kindly accept the request of adding the results of the tSNE to the manuscript which now can be found in section IIIC. In particular we can show that the two trivial 0 phases found by tSNE do indeed correspond to the points of the trivial phases TRI+ as TRI- as expected from the Referee.

Anonymous Report 1 on 2022-9-25 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202202_00047v2, delivered 2022-09-25, doi: 10.21468/SciPost.Report.5758


The authors implemented the requested changes mostly as asked. However, the strengths of the manuscript are a bit weakened in my opinion, as it is still not clear whether a topological quantity is predicted (see requested changes 1)). Instead, the authors refer to results of a future paper, not enclosed in the current manuscript. As it is the current manuscript considered for publication, not enclosed results should not matter in the decision for publication.
Nevertheless, as the rest of the manuscript has been adapted as requested and it represents a nice and exhaustive ml-based study of a topological phase transition in the presence of interactions, in my opinion it meets the criteria required for publication. I would thus recommend the paper for publication already in the current state.
If the authors still wish to improve the quality of the manuscript though, including the results they mention in the answer to "requested changes 1)" would be beneficial. This choice, however, I would leave up to the authors.

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Author:  Davide Vodola  on 2022-11-18  [id 3044]

(in reply to Report 1 on 2022-09-25)

We kindly thank the Referee for their comments. We greatly appreciate that they saw the validity of our work so that it can be published in the current form. Concerning the point raised about the learned quantity from the model, we understand the importance of such analysis and for this reason we believe it deserves further studies that will be published in a future work.

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