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Exponentially long lifetime of universal quasisteady states in topological Floquet pumps
by Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner
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Submission summary
Authors (as registered SciPost users):  Tobias Gulden 
Submission information  

Preprint Link:  https://arxiv.org/abs/1901.08385v2 (pdf) 
Date submitted:  20191122 01:00 
Submitted by:  Gulden, Tobias 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We investigate a mechanism to transiently stabilize topological phenomena in longlived quasisteady states of isolated quantum manybody systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasisteady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasisteady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's FloquetBloch bands. In such a state, all the nonuniversal properties of these bands are washed out, hence only the topological properties persist.
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Reports on this Submission
Anonymous Report 2 on 2020119 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1901.08385v2, delivered 20200119, doi: 10.21468/SciPost.Report.1462
Strengths
1. This paper addresses a topic that is timely and important. There are many proposals for realizing nontrivial topological states in Floquet systems at the level of band structure, but the stability of these in the presence of interactions is rather poorly studied. Thus the work is wellmotivated.
2. The technical arguments seem reasonable (and are analogous to other recent results on thermalization, so I am fairly confident the main steps in the proof are correct).
Weaknesses
1. There is a point I still find confusing and did not see clearly addressed in the text. If the instantaneous bands are very far apart in energy, then their hybridization to form a Floquet band is also exponentially suppressed in the same parameter Delta. The concept of a Floquet band is only sensible on timescales long compared with hybridization. The authors do not dwell on this point but it seems crucial. (Absent hybridization one cannot get a nontrivial Floquet model.)
2. Generally a little more discussion of the relevant perturbation theory would be helpful. I am not fully up to date on recent work on this topic, so I am probably missing something obvious, but since this paper is not pagelimited it has no excuse for not being selfcontained.
3. For Floquet bands with very small band gaps one would worry that a small electric field (for example) would drive diabatic transitions between the right and left pumping bands.
Report
I assume the main result is right since I cannot find concrete errors in the proofs but I am missing part of the intuition for why. It seems to be using the instantaneous band gap to control heating rates, which is fine, but it seems that this will also lead to Floquet bands with very small Floquet band gaps.
I would like the authors to consider these issues when revising.
Anonymous Report 1 on 20191228 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1901.08385v2, delivered 20191227, doi: 10.21468/SciPost.Report.1417
Report
In the manuscript by Gulden et. al, the authors analytically proved the existence of a time window in which a prethermal quasisteady state persists, given the following conditions: 1) Local Hamiltonians; 2) Singleparticle energy gap is the largest energy scale.
I find this result interesting and important, and the paper is well written, except some minor things listed below. Once fixed, the paper can be published.
 Page 5, second paragraph, i∂_t ψ ̃ ⟩=H_0 (t)ψ ̃ ⟩, H_0 (t) is not defined.
 2 lines below the above one, should the H_0 (t) have a tilde on top of it?
 Page 6, preservesthe > preserves the
 Page 6, below Eq.(4), one should define L as the length of the system.
Page 9, below Eq.(9), the authors wrote “similarly for β _k (t)”. How about θ _k (t)?
 Page 15, in Eq.(39), the authors should define V_0 (t). Is it the same as V_intra?
 Page 21, end of Appendix A, V(t) should be \mu(t)?
Author: Tobias Gulden on 20200220 [id 744]
(in reply to Report 2 on 20200119)Dear referee,
we thank you for your thorough and detailed analysis of our work! While we are preparing a response and corrections to our manuscript, we are not entirely sure which point you address with your second comment "a little more discussion of the relevant perturbation theory would be helpful". Can you please point out the relevant location(s) in our manuscript, e.g. section or equation numbers? That would be very helpful for us to address this weakness as precisely as possible.
Many thanks!