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Integrable Floquet dynamics
by Vladimir Gritsev, Anatoli Polkovnikov
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Authors (as registered SciPost users):  Vladimir Gritsev · Anatoli Polkovnikov 
Submission information  

Preprint Link:  http://arxiv.org/abs/1701.05276v3 (pdf) 
Date submitted:  20170410 02:00 
Submitted by:  Gritsev, Vladimir 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finitedimensional Lie groups and infinitedimensional generalization thereof, e.g. the Onsager algebra of the Ising model. The second class is related to the row transfer matrices of the 2D statistical mechanics models, which after analytic continuation are identified with the Floquet evolution operator. The third class of models, called here "boost models", is constructed as a periodic interchange of two Hamiltonians  one is the integrable lattice model Hamiltonian, while the second is the boost operator. The latter for known cases coincides with the entanglement Hamiltonian and is closely related to the corner transfer matrix of the corresponding 2D statistical models. It is also a generator of conserved charges in the first Hamiltonian. We present several explicit examples. As an interesting application of the boost models we discuss a possibility of generating periodically oscillating states with the period different from that of the driving field. In particular, one can realize an oscillating state by performing a static quench to a boost operator. We term this state a "Quantum Boost Clock".
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 4) on 201758 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1701.05276v3, delivered 20170508, doi: 10.21468/SciPost.Report.128
Strengths
Same as previous report
Weaknesses

Report
The authors have implemented the suggestions contained in the previous reports and I believe the paper is now almost ready for submission. However I still have some comments before publication. There are still few typos and therefore I recommend the authors to double check the manuscript again. For example:
formula 71 should contain b0 and not lambda0
Y \equiv = above eq 57
Moreover I believe that the abstract should be less technical and it should mention the possible experimental realizations of
the protocols they introduce in the manuscript (see the reports reply provided by the authors).
Finally a more general comment: In such “boost models” introduced by the authors there is a revival of the local conserved charges which implies that energy (and the other local charges) does not change between different periods and therefore there is no heating. However what can we say about the state (namely all correlation functions) a those times T_n? It is indeed now known that a Bethe state of a XXZ chain in the thermodynamic limit is not only fixed by the charges Q_n but also by the expectation values of all the quasilocal charges, (Ref [6] and J. Stat. Mech. (2016) 063101), so what can we say about these charges in these Floquet systems? Can we perhaps say that the state at time T_n is the maximal entropy state given the constrains of the local charges Q_n (as constructed in J. Stat. Mech. (2013) P07012 and Phys. Rev. Lett. 113, 117202 (2014)) ? I invite the author to provide a related discussion.
Requested changes
1)Correct typos like
formula 71 should contain b0 and not lambda0
Y \equiv = above eq 57
2)Rephrase the abstract
3)Add a discussion on the state at the times T_n during the time evolution given by the boost models.
Report #1 by Anonymous (Referee 3) on 2017424 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1701.05276v3, delivered 20170424, doi: 10.21468/SciPost.Report.120
Strengths
See previous report.
Weaknesses
See previous report.
Report
There is only one point where I am still not satisfied, which concerns the statement about the locality of the Floquet Hamiltonian. It is physically clear how the absence of heating is related to integrability, but I do not see why this has anything to do with locality. I still expect that the Floquet Hamiltonian is generally nonlocal and as far as I know this is revealed by explicit perturbation theory calculations.
However, this is not of much consequence to the new version of the paper, since it is made clear in the text that the classes of systems they present are examples rather than an exhaustive classification, and for these cases the Floquet Hamiltonian happens to be local and the integrals of motion can be found analytically.
Given that I am satisfied with the rest of their answers, I do recommend the publication of the revised version in Scipost Physics.
Requested changes
None.
Author: Vladimir Gritsev on 20170516 [id 135]
(in reply to Report 2 on 20170508)We thank our referee for careful reading, useful suggestions and interesting questions. We implemented his/her comments into a new version and added a paragraph (p.13, left column) as a reply to the first question. However, at this point we do not know if quasilocal conserved charges are important or not, so we did not speculate much on that issue.
Attachment:
ESF_III.pdf