Effects of external magnetic field and DM x-interaction on Fisher and Wigner–Yanase information correlations of thermal Heisenberg XYZ states

This study investigates the influence of temperature, the Dzyaloshinsky–Moriya (spin–orbit) interaction and an external inhomogeneous magnetic field in the x-direction on the thermal quantum information resources in general spin–spin Heisenberg XYZ states, focusing on local quantum Fisher information (LQFI), local quantum uncertainty (LQU) and concurrence correlations. The thermal behavior of quantum information quantifiers is analyzed under the influence of the spin–spin interaction, the spin–orbit interaction in the x-direction, and the uniformity and inhomogeneity of an applied external magnetic field in the x-direction. The study shows that quantum phenomena such as the sudden transition of entanglement and the appearance of stable correlations can be controlled by spin–spin and spin–orbit interactions as well as temperature. Furthermore, LQFI and concurrence correlations show greater robustness to temperature effects compared to LQU. After investigating the dependence of thermal correlations on the spin–spin interaction, the spin–orbit interaction, and the uniformity and inhomogeneity of the applied external magnetic field, we find that the enhancement of the x-spin–orbit interaction for quantum information quantifiers and the stability of the maximal correlation intervals depend on the applied external magnetic field. An increase in the uniformity or inhomogeneity of the applied magnetic field leads to a degradation of the quantum information resources, depending on the spin–orbit interaction. Finally, our results confirm that the dependence of the quantum information resources on the spin–spin couplings can be controlled by the spin–spin and spin–orbit interactions as well as by the applied external magnetic field.