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 ($T\ge 1$) 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.

15 pages, 10 figures

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