Distinct Signatures of Dynamical and Spectral Criticality in Quenched Quantum Batteries

Abstract

Criticality is widely used to enhance energy storage in quantum batteries. Two criticalities are compared here, one spectral and one dynamical. We ask two questions. Where does the enhancement that criticality brings to a quenched battery come from? And does the best charging performance require a critical point or a critical time? In the anisotropic XY chain, whose dynamics decomposes into independent momentum sectors, the weight each sector transfers to its upper level organizes the response. A closing spectral gap reshapes that weight near the closing momentum, so the stored energy responds sharply and controllably to the quench parameters. What it supplies is tunability rather than a larger maximum. A dynamical quantum phase transition (DQPT) marks the time at which the evolving state becomes orthogonal to its initial state, where the stored energy stays smooth, and equals the energy maximum when the final precession frequencies coincide, as for a flat band away from the critical field. The interacting Ising chain has no momentum sectors, yet its energy maximum and its return peak separate by a tunable margin. Weak quenches reduce the stored energy to the static susceptibility of the quenched operator. These results identify what optimization acts on, the distribution of transition weights and the spread of precession frequencies, and turn the weak-quench response into a probe of the transition order.