Tracking real-space quantum state breathing through Floquet-projector geometry

• URL: http://arxiv.org/abs/2608.13649v1
• Date: Thu, 13 Aug 2026 18:00:02 GMT
• Title: Tracking real-space quantum state breathing through Floquet-projector geometry
• Abstract summary: We present a quantum geometric theory to characterize the Floquet-Bloch states at stroboscopic times and during micromotion on equal footing.<n>Our framework builds upon time-evolved Floquet projectors that connect static quantum geometry, micromotion-operator geometry, and Floquet topology.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Periodic driving of spatially periodic quantum systems generates band structures that are absent in static crystals. We present a quantum geometric theory to characterize the Floquet-Bloch states at stroboscopic times and during micromotion on equal footing. Our framework builds upon time-evolved Floquet projectors that connect static quantum geometry, micromotion-operator geometry, and Floquet topology. To illustrate the formalism, we introduce the Floquet-projector quantum metric, which we employ to characterize the real-space breathing of localized states in a driven chiral-symmetric integrable spin chain. The Floquet-projector quantum metric, integrated over the Brillouin zone, captures the oscillatory variance during micromotion and, at symmetry-selected times, is bounded below by Floquet topological invariants. We further describe how the Floquet projector geometry enables a systematic investigation of micromotion dynamics in periodically driven lattice systems.

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