Quantum correlations and coherence in a two-qubit anisotropic XY under magnetic field

We study thermal quantum correlations and coherence in Heisenberg XY model with anisotropic interactions under a uniform magnetic field B. Using concurrence C, local quantum uncertainty (LQU), Bell-Clauser-Horne-Shimony-Holt (CHSH) nonlocality mathbb{B}, and coherence C_l as quantifiers, we analyze how magnetic anisotropy δ_m, coupling anisotropy δ_c, Dzyaloshinskii-Moriya (DM) interaction D, temperature T, and magnetic field B modulate quantum resources. At low temperatures and relevant magnetic fields, the entanglement is maximized, but exhibits sudden death for δ_m = 0, which turns into a smooth decay as δ_m increases, highlighting its stabilizing role. LQU shows that stronger anisotropy suppresses quantum correlations, while mathbb{B} induces a non-monotonic response peaking at a critical field B_c. Bell-CHSH nonlocality violations $ mathbb{B} > 2 $ persist below B_c, but thermal noise $ T geq 1 $ suppresses them. Coherence C_l is most robust to thermal fluctuations, especially for high δ_m, which also dampens abrupt quantum phase transitions. The DM interaction is essential for entanglement generation, with D and anisotropy synergistically enhancing correlation resilience. We identify a hierarchy of thermal degradation: nonlocality $ mathbb{B} $ vanishes first, followed by entanglement (C), then general quantum correlations (LQU), while coherence C_l persists the longest. These results demonstrate tunable control of quantum resources via anisotropy and external parameters, providing insights for the design of robust spin-based quantum technologies.