Dimensional enhancements in a quantum battery with imperfections

We show that the average power output of a quantum battery based on a quantum interacting spin model, charged via a local magnetic field, can be enhanced with the increase of spin quantum number, thereby exhibiting dimensional advantage in quantum batteries. In particular, we demonstrate such increment in the power output when the initial state of the battery is prepared as the ground or canonical equilibrium state of the spin-j4pt0exXY model and the bilinear-biquadratic spin-j Heisenberg chain (BBH) in presence of the transverse magnetic field and a weak value of interaction strength between the spins in the former model. Interestingly, we observe that in the case of the $XY$ model, a tradeoff relation exists between the range of interactions in which the power increases and the dimension, while for the BBH model, the improvements depend on the phase in which the initial state is prepared. Moreover, we exhibit that such dimensional advantages persist even when the battery Hamiltonian has some defects or when the initial battery state is prepared at finite temperature.