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Localization and fractality in disordered Russian Doll model

by Vedant Motamarri, Alexander S. Gorsky, Ivan M. Khaymovich

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Submission summary

Authors (as registered SciPost users): Ivan Khaymovich
Submission information
Preprint Link: scipost_202208_00079v1  (pdf)
Date accepted: 2022-09-15
Date submitted: 2022-08-29 18:08
Submitted by: Khaymovich, Ivan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, we consider a time-reversal symmetry breaking deformation of this model, known as the Russian Doll Model (RDM), and implement diagonal on-site disorder. The localization and ergodicity-breaking properties of the single-particle spectrum are analyzed using a large-energy renormalization group (RG) over the momentum-space spectrum. Based on the above RG, we derive an effective Hamiltonian of the model, discover a fractal phase of non-ergodic delocalized states -- with the fractal dimension different from the paradigmatic Rosenzweig-Porter model -- and explain it in terms of the developed RG equations and the matrix-inversion trick.

Published as SciPost Phys. 13, 117 (2022)

Author comments upon resubmission

Dear Prof. Sarang Gopalakrishnan,

Thank you for reopening the refereeing stage and for a quick editor's decision. We would like to resubmit the article for further consideration for SciPost Physics with the revision requested by the referee.
We would like to thank the Referee for taking the time to have careful read our manuscript and for their report.
We provide a point-by-point reply to the Referee comments and attach it to the Referee report.

For simplicity of tracking the changes, we use the red font for the concrete requested changes and the blue one for slight reformulations.

Sincerely yours,
Vedant R. Motamarri, Alexander S. Gorsky, and Ivan M. Khaymovich

List of changes

**Summary of changes**
- The reference [38] have been added. The other references have been shifted accordingly.
- A thorough editing of the text has been carried out as per referee's suggestion to make the exposition clearer.
- The specific phrases, mentioned by the Referee, have been corrected accordingly.

Submission & Refereeing History

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Resubmission scipost_202208_00079v1 on 29 August 2022

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