SciPost Submission Page
Refined cyclic renormalization group in Russian Doll model
by Vedant Motamarri, Ivan M. Khaymovich, Alexander Gorsky
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Ivan Khaymovich |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2406.08573v1 (pdf) |
| Date submitted: | 2024-08-21 10:18 |
| Submitted by: | Khaymovich, Ivan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We discuss the Russian Doll Model (RDM) of superconductivity for finite energy levels. Previously, cyclic renormalization group (RG) and Efimov scaling were found in RDM for part of the equidistant spectrum and we generalize this observation in a few directions. We find that when the whole spectrum is considered, equidistancy condition is removed or diagonal disorder is added, the cyclicity of RG survives but the period of RG becomes energy dependent. The analytic analysis is supported with exact diagonalization.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. Interesting subject potentially useful for many problems
2. Simple enough analysis (compared to Bethe ansatz)
3. Validity of results
Weaknesses
1. Introduction is not guided by physics and difficult to digest even by prepared readers
Report
I recommend to publish to paper after a major revision of the presentation, especially Introduction
Requested changes
Rewrite Introduction in more physics terms
Recommendation
Ask for major revision
Strengths
1. This is an interesting extension of the Russian Doll BCS model.
2. It points out how naive Efimov scaling is not necessarily exact but can depend on the energy.
3. Extensive numerical support.
Weaknesses
1. See report for minor revisions.
Report
I recommend this paper for publication after a few minor modifications.
The authors study an interesting extension, or further study of the Russian Doll BCS model. They point out that Efimov exponential scaling can be violated. Namely the RG period can be energy dependent.
Requested changes
1. The QFT model in Ref. [20] has the same RG beta function and Russian Doll resonances, where their masses are
$M_n = 2m \cosh( n \lambda )$
where $\lambda$ is the RG period.
This only has exact Efimov scaling for large n:
$M_n = m e^{n \lambda}$
Thus at low energies we don't have exact Russian Doll scaling.
Can the authors comment on whether this is related to their main result?
2. Section 3 is named "Sierra's RG..." and refers to
Refs. [19][20]. However he is one of 2 other authors in these papers, so referring to it as Sierra's RG should be corrected.
Recommendation
Ask for minor revision