Kitaev Quantum Batteries: Super-Extensive Scaling of Ergotropy in 1D Spin\(-1/2\) \(XY-\Gamma(\gamma)\) Chain

We investigate the performance of a novel model based on a one-dimensional (1D) spin-\(1/2\) Heisenberg \(XY-\Gamma(\gamma)\) quantum chain, also known as 1D Kitaev chain, as a working medium for a quantum battery (QB) in both closed and open system scenarios. We analyze the closed QB scenario by analytically evaluating ergotropy across different spin-spin couplings, anisotropies in spin interactions, Zeeman field strengths, charging field intensities, \(\Gamma\) interactions, and temperature. Our results indicate that the ergotropy is highly dependent on spin-spin coupling and anisotropy. Under variable parameters, an increase in the spin-spin coupling strength displays quenches and exhibits non-equilibrium trends in ergotropy. After a quench, ergotropy may experience a sharp increase or drop, suggesting optimal operational conditions for QB performance. In the open QB scenario, we examine spin chains of sizes \(2 \leq N \leq 8\) under the influence of dephasing, focusing on the evolution of ergotropy. We study two charging schemes: parallel charging, where spins are non-interacting, and collective charging, involving spin-spin coupling. In the former, increased Zeeman field strength enhances both the peak ergotropy and charging rate, although without any quantum advantage or super-extensive scaling. In the latter, increasing spin-spin coupling might not achieve super-extensive scaling without introducing anisotropy in the spin-spin interaction. Our results suggest that optimal QB performance and a quantum advantage in scaling can be achieved by leveraging anisotropic spin-spin couplings and non-zero \(\Gamma\) interactions, allowing for faster charging and higher ergotropy under super-extensive scaling conditions up to \(\alpha=1.24\) for the given size of the spin chain.