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Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
by Sreemayee Aditya, Diptiman Sen
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Submission summary
| Authors (as registered SciPost users): | Sreemayee Aditya |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202305_00023v2 (pdf) |
| Date submitted: | 2023-08-11 08:19 |
| Submitted by: | Aditya, Sreemayee |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study if the interplay between dynamical localization and interactions in periodically driven quantum systems can give rise to anomalous thermalization behavior. Specifically, we consider one-dimensional models with interacting spinless fermions with nearest-neighbor hopping and density-density interactions, and a periodically driven on-site potential with spatial periodicity m=2 and m=4. At a dynamical localization point, these models evade thermalization either due to the presence of an extensive number of conserved quantities (for weak interactions) or due to the kinetic constraints caused by drive-induced resonances (for strong interactions). Our models therefore illustrate interesting mechanisms for generating constrained dynamics in Floquet systems which are difficult to realize in an undriven system.
Author comments upon resubmission
We are hereby resubmitting our paper. We have responded in detail to all the comments by
the two referees and we have made appropriate changes in the manuscript. The list of changes
is given below.
We would like this paper to be considered for SciPost Physics only, not for SciPost Physics Core.
We believe that with the extensive changes that we have made in the manuscript and our detailed
responses to each of the referees' comments, the referees will agree that SciPost Physics is the
appropriate journal for this paper.
Sincerely,
Sreemayee Aditya
Diptiman Sen
List of changes
We have shown the major changes in blue in the revised manuscript.
1. We have added two sections, namely, the thermodynamic stability of Hilbert space fragmentation in this class of models
(Sec. 5) and the experimental accessibility (Sec. 6).
2. We have added the derivation of the third-order effective Hamiltonian at the dynamical localization point in Appendix C.
This is relevant for answering a question asked by the first referee.
3. We have removed Fig. 1 (b). However we have retained Fig. 1 (c), which is important for seeing the variation of the
bandwidth due to the third-order corrections which become larger when the value of mu is decreased.
4. We have added two figures (Figs. 23 (a) and (b)) showing the variation of the Loschmidt echo with time for the resonant
case of the period-2 model at a dynamical localization point for two sets of parameter values. We have numerically fitted
the envelop of the Loschmidt echo varying with time to extract the decay rate of the envelop and have discussed how the
decay rate is related to the parameter values used.
5. We have added a figure (Fig. 2 (e)) showing how the crossover scale n_c diverges as one approaches the critical frequency
omega_c from the omega > omega_c side. This further confirms our analytically derived result.
6. We have added a figure (Fig. 5 (c)) showing a plot of E_exact vs E_FPT for the resonant case of the period-2 model at
a dynamical localization point. We have fitted the plot to quantify the agreement of the first-order Floquet perturbation
theory with the numerically obtained results.
7. We have mentioned certain symmetries of our effective Floquet Hamiltonian obtained for the period-2 model at resonance
and at a dynamical localization point to contrast this kind of Hilbert space fragmentation (HSF) with the models showing
HSF which were known earlier.
8. We have corrected some typos pointed out by the referees.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023-8-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202305_00023v2, delivered 2023-08-25, doi: 10.21468/SciPost.Report.7710
Strengths
1- Very well written
2- Nice combination of analytical and numerical work
Weaknesses
1- Results potentially only valid in high frequency regime.
2- Insufficient pixel resolution of figures.
Report
The authors have carefully addressed all comments by the referees and significantly improved and extended the paper.
One major claim of the paper is the stability of dynamical localization in the presence of interactions and the authors have added an analysis as a function of system size in Sec. 5. Unfortunately, this analysis was only carried out in the high frequency regime ($\omega=20$) and it remains unclear whether the discussed phenomena are stable in the thermodynamic limit.
It is well known in Floquet many-body systems that for fixed driving frequency, most systems become ergodic in the limit of large system sizes. This limit is, however, not reachable in practice for high frequencies of the drive. From Fig. 22, I would conclude that the results are very far from the thermodynamic limit, because the density of states is still strongly peaked on the unit circle. However, there are some slight indications in the $L=20$ results in Fig 22. c), that at the edge of the quasienergy spectrum an interference between states at high and low quasienergy starts to take place, "bending up" the entanglement curve. I suspect that in the limit of larger sizes (or, much easier to analyze, at lower driving frequency), the density of states will become flat and potentially the system will be ergodic.
Only in this limit, if the system indeed escapes ergodicity as the authors claim, will the results be convincing in all claimed generality.
This being said, the results and discussion stand on their own and are of course valid at the analyzed system sizes and driving frequencies. It would be good to explicitly say that the results apply for fast driving, though.
In summary, I can recommend this paper for publication in SciPost Physics Core. I cannot recommend publication in SciPost Physics, because of the remaining doubts on the generality of the results in the thermodynamic limit as explained above. This concern prevents fulfilling the acceptance criteria of SciPost Physics.
Requested changes
1- This paper can only be published when the rendering quality of the figures is improved in the production stage.
Report
The authors have improved the overall motivation of their study and convincingly argued their case w.r.t. the novelty of their results. Given the plethora of phenomena in their model which are explained in a step by step pedagogical manner, I can recommend the publication in SciPost Physics.
Author: Sreemayee Aditya on 2023-09-21 [id 3997]
(in reply to Report 1 on 2023-08-17)We would like to thank the referee for recommending our paper in SciPost Physics.
Author: Sreemayee Aditya on 2023-09-21 [id 3996]
(in reply to Report 2 on 2023-08-25)Please see the file attached below for the detailed responses.
Attachment:
ref_response_210923.pdf