# An ideal rapid-cycle Thouless pump

### Submission summary

 As Contributors: Savvas Malikis Arxiv Link: https://arxiv.org/abs/2104.02751v3 (pdf) Date accepted: 2022-06-09 Date submitted: 2022-05-03 11:48 Submitted by: Malikis, Savvas Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Mathematical Physics Approach: Theoretical

### Abstract

Thouless pumping is a fundamental instance of quantized transport, which is topologically protected. Although its theoretical importance, the adiabaticity condition is an obstacle for further practical applications. Here, focusing on the Rice-Mele model, we provide a family of finite-frequency examples that ensure both the absence of excitations and the perfect quantization of the pumped charge at the end of each cycle. This family, which contains an adiabatic protocol as a limiting case, is obtained through a mapping onto the zero curvature representation of the Euclidean sinh-Gordon equation.

Published as SciPost Phys. 12, 203 (2022)

### List of changes

In this new version, we added Section 2 explaining the take-home message of our paper.
Reading the reports, we realized that the previous version was hard to read, since it had the structure of a mathematical physics paper, even though it presents a physically remarkable result. Thus to make it accessible, without sacrificing the rigorous derivations, we added that part.

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 203 (2022)

Resubmission 2104.02751v3 on 3 May 2022
Submission 2104.02751v2 on 3 September 2021

## Reports on this Submission

### Anonymous Report 2 on 2022-5-19 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2104.02751v3, delivered 2022-05-19, doi: 10.21468/SciPost.Report.5099

### Strengths

Exact results
Well written introduction

### Weaknesses

Fine-tuning required for protocol means the result have limited physical impact

### Report

The clarity of the manuscript is significantly improved; the new version of the manuscript is clearly structured and well-written. The addition of the new Sec II makes the physics of the result much more clear, without sacrificing the rigor.

While the physical impact of the results is limited due to the fine-tuning required, the simple form of the exact charge-pumping protocol may be of use for further theoretical studies.

I have no more reservations recommend the manuscript for publication.

• validity: top
• significance: ok
• originality: good
• clarity: good
• formatting: reasonable
• grammar: good

### Anonymous Report 1 on 2022-5-17 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2104.02751v3, delivered 2022-05-17, doi: 10.21468/SciPost.Report.5088

### Strengths

Solid derivation and mathematical proofs
Well written introduction which summarizes the results and clarifies their limitations

### Weaknesses

Not generalizable. limited impact

### Report

I would like to thank the authors for their detailed response. I found the new introduction and overview sections very helpful and very well written.
It is now clarified that the finite frequency protocol suggested in the manuscript is in fact fine tuned and “engineered” such as to lead to quantized pumped charge without noise generation. Consequently, any deviations from the fine tuned limit would most probably result in noise generation and loss of quantization.

As a result of the protocols being fine tuned, I find the implications of the work on the field of topological quantum pumping somewhat limited since they cannot be generalized to more realistic scenarios, and are most likely not immediately relevant for experiments. Moreover, the manuscript does not allude to any physical intuition as to why the chosen protocols avoid excitations (although the analogy of to the quantum brachistochrone seems intriguing).

In conclusion, I believe that the topic is very interesting, the work is solid and while the immediate implications of the results are limited, they offer perspective for followup work on the topic of protected finite frequency pumping. I therefore recommend the manuscript for publication.

• validity: high
• significance: ok
• originality: high
• clarity: high
• formatting: good
• grammar: good

In particular, in Eq. 8 it is $\dot v(\tau)$ (instead of $v(\tau)$).
Also in the second half of Eq. 12 for the $t_{1,2}$ term, on the numerator it is $V(\tau)$( instead of $v(\tau)$).