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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_00023v3 (pdf) |
| Date accepted: | 2023-11-09 |
| Date submitted: | 2023-09-21 08:06 |
| 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
Dear Editor,
We are hereby resubmitting our paper in Scipost Physics. In response to the second referee’s comment regarding the generality of Hilbert space fragmentation mechanism in the lower frequency regime, we have now further analyzed the model in this limit both analytically and numerically, and we have made appropriate changes in the manuscript. The list of changes is given below.
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The pixel resolution of the figures has been improved in the revised manuscript. All the figures are now in pdf format as requested by the Editor.
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To understand HSF in the intermediate and lower frequency regimes, we have examined the period-2 model both analytically and numerically by considering the other DL points at the resonance condition. We have included Figs. 8 and 9 in the revised version of the manuscript, where the entanglement spectrum and the dynamics of Loschmidt echo are investigated in the intermediate and lower frequency regimes.
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We have added Fig. 12 showing the results for different system sizes to confirm the thermodynamic stability of the low-entanglement states in the lower frequency regime. This implies non-ergodic behavior of the system in the lower frequency regime.
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We have added Fig. 13 in the revised manuscript showing two ergodic to non-ergodic crossovers in terms of the half-chain entanglement entropy at the 2000-th stroboscopic number as a function of the driving amplitude occurring in the high-frequency and low to intermediate frequency regimes at the first and ninth dynamical localization points with resonances, respectively.
We believe that with the changes that we have made in the manuscript and our detailed responses to the referee’s comments, the second referee will agree that SciPost Physics is the appropriate journal for this paper.
Sincerely,
Sreemayee Aditya
Diptiman Sen
List of changes
1. The pixel resolution of the figures has been improved in the revised manuscript. All the figures are now in pdf format as requested by the Editor.
2. To understand HSF in the intermediate and lower frequency regimes, we have examined the period-2 model both analytically and numerically by considering the other DL points at the resonance condition. We have included Figs. 8 and 9 in the revised version of the manuscript, where the entanglement spectrum and the dynamics of Loschmidt echo are investigated in the intermediate and lower frequency regimes.
3. We have added Fig. 12 showing the results for different system sizes to confirm the thermodynamic stability of the low-entanglement states in the lower frequency regime. This implies non-ergodic behavior of the system in the lower frequency regime.
4. We have added Fig. 13 in the revised manuscript showing two ergodic to non-ergodic crossovers in terms of the half-chain entanglement entropy at the 2000-th stroboscopic number as a function of the driving amplitude occurring in the high-frequency and low to intermediate frequency regimes at the first and ninth dynamical localization points with resonances, respectively.
Published as SciPost Phys. Core 6, 083 (2023)