This study explores the thermal quantum-memory-assisted entropic uncertainty relation (QM-EUR) and entanglement in a general two-qubit XYZ-Heisenberg spin chain model in the presence of the Dzyaloshinskii-Moriya (DM) interaction. The characterization of y-component DM and spin-spin interactions are particularly focused. It is found that the DM and spin-spin interaction strengths highly regulate the flow behavior and the initial final levels of QM-EUR and entanglement. In comparison, the spin-spin interaction strength in the z-direction remains useful in both ferromagnetic and anti-ferromagnetic regimes for entropic uncertainty suppression and entanglement generation. Additionally, the negative and the positive y-directed DM values can usefully turn classical states into resourceful quantum states. The dynamics of thermal QM-EUR and entanglement-of-formation have symmetric behaviors only with respect to y-component DM and z-component spin-spin interaction. Finally, different critical points of temperature, y-component DM as well as spin-spin interaction are encountered, which should be opted to preserve quantum correlations and degrade uncertainty.

This paper investigates the dynamics of two-spin nonlocality generation in a Heisenberg XXX chain with Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. We analyze the two-spin nonlocality dynamics by using uncertainty-induced nonlocality, maximal Bell inequality, and log-negativity. We demonstrate that a separable two-spin Heisenberg XXX chain state, induced by two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions, could evolve to maximal two-spin nonlocality state. The ability of preserving the maximal uncertainty-induced nonlocality can be enhanced by increasing the coupling strength of the spin-spin interaction coupling. The hierarchy principle is maintained for the two-spin Bell nonlocality and log-negativity entanglement. The two-spin log-negativity dynamics exhibits the phenomenon of sudden death and birth as a result of the intrinsic decoherence, which also causes a reduction in the two-spin nonlocalities. The two-spin uncertainty-induced nonlocality is more robust, against the intrinsic decoherence, than the other types of the nonlocality. The results indicate that by boosting the two-spin antiferromagnetic interaction, the produced nonlocalities (resulting from the DM and KSEA x-component interactions) can be shielded from the intrinsic decoherence effect.