Ayan Sahoo, Debraj Rakshit

We study discrete time-crystalline (DTC) phases in one-dimensional spin-1/2 chains with power-law interactions under periodic Floquet driving. By generalizing Stark localization to power-law interaction profiles, we identify robust period-doubled dynamics across a wide range of interaction exponents, stabilized by the interplay between coherent driving and spatially varying coupling. Within the DTC phase, the energy stored in the system, interpreted as a quantum battery, increases superlinearly with system size, although no scaling advantage persists in normalized power. Beyond energy storage, we demonstrate that the DTC phase supports enhanced quantum sensing. The quantum Fisher information associated with estimating timing deviations in the drive scales superextensively with system size, surpassing the Heisenberg limit. The degree of quantum advantage can be tuned by varying the interaction exponent, though DTC behavior remains robust throughout. Our results position power-law interacting Floquet systems as robust platforms for storing quantum energy and achieving metrological enhancement.