Abstract The concepts of concurrence, 3-steerability, and Clauser–Horne–Shimony–Holt (CHSH) inequality are employed to investigate the environmental impacts on the quantum correlations of the two-spin-1/2 Heisenberg XYZ chain model. In particular, the effects of a homogeneous magnetic field, symmetric cross interaction, and dipole–dipole interaction on the entanglement, degree of steerability, and non-locality are discussed. Results show that the entanglement and steering phenomena are bounded by the non-locality for both positive and negative values of dipole–dipole coupling. It has also been observed that higher symmetric cross-interaction strengthens the quantum correlations, whereas the homogeneous magnetic field weakens the quantumness of the system. The findings indicate that a magnetic field normal to the magnetic dipole yields better quantum correlations than when they are parallel.
Quantum correlations between a pair of spin-1/2 represented by an XYZ-Heisenberg chain are investigated under symmetric, anti-symmetric and long-range dipolar interactions. Entanglement, steering, and nonlocality are quantified through concurrence, 3-steering functions, and normalized Bell functions, respectively. By modulating interaction directions, effects on quantum correlations are elucidated for two scenarios: dipolar coupling along x or z, with symmetric and anti-symmetric terms oriented perpendicular or parallel. The results indicate that quantum correlations are enhanced when dipolar coupling aligns with the z-direction versus the x-direction. Moreover, increasing long-range dipolar interaction strength degrades the quantum correlations for weaker Heisenberg chain coupling. Positioning symmetric and anti-symmetric couplings along the z-direction affect quantum correlation dissipation at a critical point. Furthermore, with symmetric and anti-symmetric terms oriented along x, quantum correlations diminish for x-direction dipolar coupling.
Abstract This paper investigates quantum correlations between two identical spin-1/2 particles linked by long-range dipolar interactions. A time-dependent symmetric cross-spin interaction and an external homogeneous magnetic field that varies with time are also applied to the system. Quantum correlations, such as entanglement, steering, and steered quantum coherence, are quantified using concurrence, three-steering functions, and the l 1 norm measure of coherence, respectively. These quantum correlations are examined based on the direction of interaction for dipole–dipole interactions along either the x-axis or z-axis and are symmetric concerning Zeeman energy along these axes. The maximal bounds of all three quantifiers are obtained by increasing the frequency of the time-dependent and symmetric coupling parameters. These maximal bounds significantly strengthen when considering symmetric and Zeeman interactions along the x-axis; however, the pinnacle of entanglement is reached in perpendicular configurations.
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
Cl 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−CHSHnonlocalityviolations( \mathbb{B} > 2 $) persist below $ B_c
,butthermalnoise( T \geq 1 $) suppresses them. Coherence $ C_l $ is most robust to thermal fluctuations, especially for high
δm, 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}
)vanishesfirst,followedbyentanglement( 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.
In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.
In this paper, we explore nonlocal correlation and Bell non-locality in a two-qubit Heisenberg XYZ model by using Bell-CHSH inequality and uncertainty induced nonlocality (UIN) as well as log-negativity. We consider the effects of spin-qubits XYZ-Heisenberg couplings, the y-component of DM interaction, and intrinsic decoherence. Our results show that spin-qubits Heisenberg couplings have a strong ability to create two-qubit nonlocal correlations, enhanced by combining with DM interactions. The generated Bell-CHSH nonlocality and entanglement conform to the hierarchy principle. The UIN correlation is more resistant to intrinsic decoherence compared to Bell-CHSH inequality and log-negativity. Intrinsic decoherence causes the disappearance of Bell-CHSH non-locality and log-negativity entanglement, while leading to the appearance of partial stationary spin-qubits UIN correlation.
The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the J i (i-axis spin-spin interaction), the higher critical value the B i (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger J i corresponds to more entanglement, while in the strong-field regime, different J i correspond to the same entanglement. In addition, it is found that with the increase of J i , the concurrence can approach the maximum value more rapidly for the smaller B i , and can reach a larger value for the smaller b i (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction J i , or by decreasing the uniform magnetic field B i and the nonuniform magnetic field b i .