Floquet Supersymmetry

TL;DR

This paper introduces Floquet supersymmetry, a novel nonequilibrium phenomenon in periodically driven quantum systems, revealing symmetry-based bounds on state degeneracies and observable signatures like period-doubling.

Contribution

It demonstrates how time-reflection symmetry in Floquet systems leads to supersymmetry analogues, including bounds on quasienergy degeneracies and fermion-boson interchange, with robust models and experimental signatures.

Findings

Existence of Floquet Witten index bounds quasienergy degeneracies.

Time reflection symmetry can interchange fermions and bosons.

Observable period-doubling effect as a signature of Floquet supersymmetry.

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.