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arXiv · 1706.05303

Universal fluctuations of Floquet topological invariants at low frequencies

M. Rodriguez-Vega·B. Seradjeh
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Abstract

We study the low-frequency dynamics of periodically driven one-dimensional systems hosting Floquet topological phases. We show, both analytically and numerically, in the low-frequency limit $Ω\to0$, the topological invariants of a chirally-symmetric driven system exhibit universal fluctuations. While the topological invariants in this limit nearly vanish on average over a small range of frequencies, we find that they follow a universal Gaussian distribution with a width that scales as $1/\sqrtΩ$. We explain this scaling based on a diffusive structure of the winding numbers of the Floquet-Bloch evolution operator at low frequency. We also find that the maximum quasienergy gap remains finite and scales as $Ω^2$. Thus, we argue that the adiabatic limit of a Floquet topological insulator is highly structured, with universal fluctuations persisting down to very low frequencies.

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M. Rodriguez-Vega, B. Seradjeh. 2018-05-08. Universal fluctuations of Floquet topological invariants at low frequencies. https://doi.org/10.1103/physrevlett.121.036402

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