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arXiv · 1710.05927

Floquet Supersymmetry

Thomas Iadecola·Timothy H. Hsieh
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Abstract

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical sypersymmetry. In particular, we find Floquet analogues of the Witten index that place lower bounds on the degeneracies of states with quasienergies $0$ and $\pi$. Moreover, we show that in some cases time reflection symmetry can also interchange fermions and bosons, leading to fermion/boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies $0$ and $\pi$, which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.

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Thomas Iadecola, Timothy H. Hsieh. 2017-10-16. Floquet Supersymmetry. https://doi.org/10.1103/physrevlett.120.210603

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