Locked Subharmonic Oscillations in the Entanglement Spectrum of a Periodically Driven Topological Chain

Abstract: Periodically driven quantum systems can exhibit subharmonic response, usually characterized through physical observables and often discussed in interacting settings. Here we show that a sharp subharmonic signature already appears in the entanglement spectrum of a number-conserving free-fermion system. We study a two-step driven Su-Schrieffer-Heeger chain whose Floquet operator supports symmetry-protected edge modes at quasienergies $0$ and $π$. When the initial state is a coherent superposition of these two edge sectors, the subsystem correlation matrix alternates between two stroboscopic structures, and an overlap-tracked single-particle entanglement level distills a robust period-doubling response with Fourier weight concentrated at half the drive frequency. By contrast, diagonal edge densities remain flat by sublattice symmetry, while an off-diagonal edge-bond observable provides the corresponding linear one-body comparator. The effect disappears both when the initial state is replaced by a stroboscopically stationary Floquet eigenstate built from the same topological mode content, and when the system is placed in the topologically trivial phase where no edge modes exist. Altogether, these establish zero-$π$ Floquet topology as a necessary condition and coherent nonequilibrium preparation as the additional sufficient ingredient. Our results identify entanglement spectroscopy as a sharp subsystem-resolved probe of Floquet topological coherence.