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Flow Equations for Disordered Floquet Systems
by S. J. Thomson, D. Magano, M. Schiró
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Submission summary
| Authors (as registered SciPost users): | Steven Thomson |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2009.03186v2 (pdf) |
| Date submitted: | 2020-12-23 10:30 |
| Submitted by: | Thomson, Steven |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.
Author comments upon resubmission
We shall respond to the Referee’s points in detail in our Author Reply, however we wish to clearly state here that our identification of the delocalization transition in the driven Anderson insulator is not erroneous, or in conflict with any of the existing literature: the previous studies that the Referee cites used a monochromatic drive, however in the present work we use a step-like drive which has dramatically different effects.
In our revised manuscript, we clearly address this discrepancy with an additional new Appendix C. We have also added further discussion about resonances in both the interacting and non-interacting models, and have improved the clarity and presentation of our results throughout.
List of changes
i) We have added a new figure (Fig. 7 of the revised manuscript) which quantitatively demonstrates how the relative error in the many-body quasienergies changes with drive frequency.
ii) Added an Appendix B3 which shows the calculation for the flow of the interaction terms.
iii) New Appendix C, including a new Fig. 9, which discusses the differences between monochromatic and step-like drive protocols, with new numerical results to clearly demonstrate that our findings are consistent with previous work.
iv) New paragraph below Eq. 27 discussing resonances in non-interacting systems, and a brief discussion of resonances in intearacting systems added below Eq. 39.
v) Other minor changes: all figures updated to be in vector graphics format, all frequencies are now normalised by the disorder bandwidth, and other minor typographical edits throughout.