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

Abstract

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 $ \delta_m $, coupling anisotropy $ \delta_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 $ \delta_m = 0 $, which turns into a smooth decay as $ \delta_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 \( \delta_m \), 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.