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Arrested Development and Fragmentation in Strongly-Interacting Floquet Systems

by Matthew Wampler, Israel Klich

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Submission summary

Authors (as registered SciPost users): Matthew Wampler
Submission information
Preprint Link: scipost_202210_00045v2  (pdf)
Date accepted: 2023-04-06
Date submitted: 2023-01-23 22:06
Submitted by: Wampler, Matthew
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We explore how interactions can facilitate classical like dynamics in models with sequentially activated hopping. Specifically, we add local and short range interaction terms to the Hamiltonian and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution, and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion.

Published as SciPost Phys. 14, 145 (2023)

Author comments upon resubmission

Dear Editor,

We hereby resubmit our paper for your consideration. We thank the referees for a close reading of the manuscript. We believe we have answered the questions of the referees whose inquiries prompted us to improve the presentation, add a new section investigating the entanglement entropy and level statistics of the Hubbard-RLBL model in 2D, introduce a new measure which describes the proximity of a given evolution to a complex permutation of number states, and add a description of the scaling of the number of frozen states in our 1D Hubbard example. In addition, we have also added several smaller clarifying remarks as suggested by the referees. With these additions, and given the positive remarks of the referees regarding the interest and relevance of our results, we believe our paper is now ready to be published in SciPost Physics.

The Authors

List of changes

- New section (3.4) investigating entanglement entropy and level statistics in the Hubbard-RLBL in 2D
- In section (2.3) we introduce a new measure which provides a qualitative estimate of the proximity of a given evolution to a complex permutation. Additionally, we provide a plot of this quantity, Fig. 3, in order to better illustrate the appearance of the special Diophantine points in the Hubbard-RLBL model
- In section (3.3) we add a description of the scaling of the number of frozen states for our 1D Hubbard example
- We have rewritten much of section (3.1) to improve clarity as requested by referee 2
- An addition to the summary and discussion section (4) on the effects of long range interactions
- A remark at the end of appendix A.2 on why m0 (in equation 34) is always even
- A brief summary (added to section 3.2) of the arguments from Refs 49 and 50 regarding the expectation that disorder might stabilize the dynamics at the special points in some cases
- A remark (added to section 2.5) on our conjecture that there exist a solution to equation (32) for any Dmax
- A comment in section 2.6 to clarify the distinction between the NN-RLBL model and the measurement-induced chirality model with nearest neighbor interactions
- A comment added at the start of section 2.2 suggesting a reader familiar with Diophantine equations may skip the section
- We fixed a few miscellaneous errata/typos including all of those noted by the referees

Reports on this Submission

Anonymous Report 1 on 2023-2-12 (Invited Report)


The authors have addressed my remarks.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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