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The Vosk-Altman Strong Disorder Renormalization for the unitary dynamics ofvarious random quantum spin chains is reformulated as follows : the localdegree of freedom characterized by the highest eigenfrequency $\Omega$ can beconsidered as a high-frequency-Floquet-periodic-driving for the neighboringslower degrees of freedom. Then the two first orders of the high-frequencyexpansion for the effective Floquet Hamiltonian can be used to generate theemergent Local Integrals of Motion (LIOMs) and to derive the renormalizationrules for the effective dynamics of the remaining degrees of freedom. The flowfor this effective Floquet Hamiltonian is equivalent to the RSRG-X procedure toconstruct the whole set of eigenstates that generalizes the Fisher RSRGprocedure constructing the ground state. This general framework is applied tothe random-transverse-field XXZ spin chain in its Many-Body-Localized phase, inorder to derive the renormalization rules associated to the elimination of thebiggest transverse field and to the elimination of the biggest couplingrespectively.

journal of physics. a, mathematical and theoretical

Strong Disorder Renormalization for the dynamics of Many-Body-Localized  systems : iterative elimination of the fastest degree of freedom via the  Floquet expansion