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Renormalization to localization without a small parameter

by A. G. Kutlin, I. M. Khaymovich

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Submission summary

Authors (as registered SciPost users): Ivan Khaymovich · Anton Kutlin
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-03-25
Date submitted: 2020-03-20 01:00
Submitted by: Kutlin, Anton
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational


We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.

Author comments upon resubmission

Dear Editor,

Thank you for providing us the reports both of Prof. Burin and of the second Referee.
We would like to resubmit the article entitled “Renormalization to localization without a small parameter” for consideration in SciPost Physics.

First of all, we would like to thank both Referees for their careful reading of the manuscript, for providing constructive criticism, and for their positive comments. We hope that our responses and changes made to the manuscript have convinced both Prof. Burin and the second Referee so that the manuscript is now considered suitable for the publication in SciPost Physics.

Yours sincerely,

Anton G. Kutlin and Ivan M. Khaymovich

List of changes

In order to improve the manuscript, we follow the recommendations of the Referees and make the following changes in the manuscript:
1. Following the comment of Prof. Burin, we have modified Fig. 7 by showing the points of the maxima of all curves in the linear scale in the insets. We emphasize the same points in the main panels by full circles and the same dashed fitting lines as in the insets.
2. Following the first comment of the second Referee, we have reduced the number of repetitive citations of the previous papers and explained the terms “matrix-inversion trick” and “the duality”.
3. We have also clarified in the introduction what is similar and what is different in our paper from the previous works.
4. The “renormalization time” has been replaced by the “renormalization scale” throughout the text.
5. The footnotes have been moved from the Reference list to the text.
6. The phrase starting with "this significantly reduces …" has been corrected and the corresponding discussion has been added.
7. In addition, we have added some relevant references and discussed the surprises of the Anderson and many-body localization in a little bit more detailed manner.
Regarding the suggestion of Prof. Burin to add more numerical data for the PLE model, we added a reference to the paper [32] which already contains all the data. We think that inverse participation ratio and level statistics do not directly connect to the discussed analytical method and will unnecessarily complicate and enlarge the paper.

Published as SciPost Phys. 8, 049 (2020)

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