A comparative study of quantum resources in bipartite Lipkin-Meshkov-Glick model under DM interaction and Zeeman splitting

We assess the thermal resilience of key quantum resources-(ℓ1)-norm coherence (Q), quantum discord (D), logarithmic negativity (LN), Bell nonlocality (B), and quantum steering (S)-in a bipartite Lipkin-Meshkov-Glick (LMG) spin system subject to competing Dzyaloshinskii- Moriya (DM) interactions and Zeeman splitting. By varying temperature (T), spin-spin coupling (λ), magnetic field strength (B0), and DM amplitude (Dz), we reveal a clear hierarchy of thermal stability: coherence and discord remain robust well beyond the temperatures at which nonlocality (B), steering (S), and bipartite entanglement (LN) undergo successive thermal collapse. Stronger spin-spin coupling λ and nonzero DM strength D ≥ 0 z not only amplify overall quantum correlations but also elevate the critical temperatures Tc for the survival of each resource. In contrast, a large B0 polarizes the spins into paramagnetic states, thereby suppressing all quantum features at fixed T. Notably, high amplitude of DM interactions preserves residual coherence and discord even in the high-temperature limit (T ≫ Tc). These results establish practical operating thresholds for LMGbased quantum technologies in thermal environments and highlight Dz as a powerful tuning parameter for engineering thermally robust quantum resources.