## SciPost Submission Page

# Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

### by Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner

#### This is not the current version.

### Submission summary

As Contributors: | Tobias Gulden |

Arxiv Link: | https://arxiv.org/abs/1901.08385v2 (pdf) |

Date submitted: | 2019-11-22 |

Submitted by: | Gulden, Tobias |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### Abstract

We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 2 on 2020-1-19 Invited Report

### 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 well-motivated.

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 page-limited it has no excuse for not being self-contained.

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 2019-12-28 Invited Report

### Report

In the manuscript by Gulden et. al, the authors analytically proved the existence of a time window in which a prethermal quasi-steady state persists, given the following conditions: 1) Local Hamiltonians; 2) Single-particle 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)?

(in reply to Report 2 on 2020-01-19)

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!