Geometric Floquet theory

• URL: http://arxiv.org/abs/2410.07029v2
• Date: Thu, 16 Jan 2025 11:04:36 GMT
• Title: Geometric Floquet theory
• Authors: Paul M. Schindler, Marin Bukov,
• Abstract summary: We derive Floquet theory from quantum geometry. We show that Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates.
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• Abstract: We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential $U(1){\mapsto}\mathbb{Z}$. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifying a unique Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands. We exemplify the features of geometric Floquet theory using an exactly solvable XY model and a non-integrable kicked Ising chain. We elucidate the geometric origin of inherently nonequilibrium effects, like the $\pi$-quasienergy gap in discrete time crystals or $\pi$-edge modes in anomalous Floquet topological insulators. The spectrum of the average-energy operator is a susceptible indicator for both heating and spatiotemporal symmetry-breaking transitions. Last, we demonstrate that the periodic lab frame Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates. This work directly bridges seemingly unrelated areas of nonequilibrium physics.

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