Optimal parameter combinations of entanglement in the general Heisenberg model

Thermal entanglement, as influenced by interaction parameters, is investigated within the general Heisenberg XYZ model. We calculate the relationship between entanglement and the system interaction parameters, including spin–spin interaction parameters (SSIPs) and spin–orbit interaction parameters (SOIPs). By considering various parameter orientations, we identify four optimal combinations of the SSIPs and find that the optimal vector of the spin–orbit interaction aligns with the coordinate axis corresponding to the maximal SSIP component. Furthermore, we obtain three effective optimal combinations of the SOIPs corresponding to the optimal SSIPs, which can maximize the system entanglement when the parameters are tuned accordingly. To demonstrate the feasibility of our results under realistic experimental conditions, we propose an optical lattice scheme with tunable parameters.