Entanglement and energy transportation in the central-spin quantum battery

Quantum battery exploits the principle of quantum mechanics to transport and store energy. We study the energy transportation of the central-spin quantum battery, which is composed of $N_b$ spins serving as the battery cells, and surrounded by $N_c$ spins serving as the charger cells. We apply the invariant subspace method to solve the dynamics of the central-spin battery with a large number of spins. We establish a universal inverse relationship between the battery capacity and the battery-charger entanglement, which persists in any size of the battery and charger cells. Moreover, we find that when $N_b=N_c$, the central-spin battery has the optimal energy transportation, corresponding to the minimal battery-charger entanglement. Surprisingly, the central-spin battery has a uniform energy transportation behaviors in certain battery-charger scales. Our results reveal a nonmonotonic relationship between the battery-charger size and the energy transportation efficiency, which may provide more insights on designing other types of quantum batteries.