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.

5+4 pages, 3+1 figures. v2 includes additional connections with SUSY and a new Appendix containing a discussion of robustness to time-reflection-breaking perturbations. This version accepted to PRL

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Cited by in corpus (11)

• Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
• Spatial-Translation-Induced Discrete Time Crystals
• Homogeneous Floquet time crystal from weak ergodicity breaking
• Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
• Gauging anomalous unitary operators
• Asymmetric butterfly velocities in Hamiltonian and circuit models
• Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder
• Clean two-dimensional Floquet time-crystal
• Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
• Automated detection of symmetry-protected subspaces in quantum simulations
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system