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American Journal of Physics and Applications

Dynamic Evolution of Quantum Correlations with PSO Algorithm in the Three-qubit Heisenberg XYZ Model Considering DM and KSEA Interactions

Song Jon, Yibang Han, Jyongguang He, Kim Jyongyon, Daehong Ryang

Published Dec 19, 2025• 0 citations
Publisher

Abstract

In this paper, we consider the three-qubit Heisenberg XYZ model considering DM interaction and KSEA interaction. We use the concurrence, geometric quantum discord, and local quantum uncertainty between the first and third spin as quantum correlation measures. In the absence of a magnetic field and in the presence of a constant magnetic field, quantum correlations appear sudden death and birth, and exhibit a random behavior. In summary, the Heisenberg XYZ model, no adjustment of the exchange interaction strength, DM interaction strength, KSEA interaction strength, and external magnetic field can eliminate the sudden death and births in the evolution of quantum correlations. Thus, we use the particle swarm optimization algorithm (PSO) to determine the magnetic field strength at each time step to increase the quantum correlation. The numerical simulation results show that the quantum correlation increases and reaches a maximum value by our method, and the quantum correlation remains constant at a maximum even after the external magnetic field is cancelled. This result shows that, for any exchange interaction strength, DM interaction strength, and KSEA interaction strength, the quantum correlations reach a certain value and remain at their maximum after the magnetic field is quenched, once the time-varying magnetic field is properly designed. This result provides sufficient possibilities for the use of Heisenberg spin chains as quantum channel.

DOI
10.11648/j.ajpa.20251306.13

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We introduce a new framework for quantum two-spin correlations based on a quantum skew information quantity and long-negativity. The quantum correlations for an anisotropic two-qubit Heisenberg [Formula: see text] model are affected by physical parameters such as intrinsic decoherence, Werner states and time-dependent magnetic fields. In particular, the joint effects of Werner states, magnetic fields and anisotropic parameters on quantum correlation robustness are investigated in the presence of intrinsic decoherence. For an initially uncorrelated state, robust entanglement is generated while skew information between the two quantum bits no longer exists. It is shown that the magnetic field makes the system strongly correlated with incredibly significant steady-state values in uncorrelated states. The phenomenon of sudden death and sudden birth appear during the evolution process of initial conditions. Finally, if the system starts from a mixed state or a Werner state, the magnetic field does not play a significant role in the monotonically decreasing correlations. By leveraging our framework, one can create a kind of stability between the uncertainty-induced quantum nonlocality and the local quantum uncertainty correlations.
This study explores the dynamics of the formation of quantum correlations, namely: local quantum Fisher information and concurrence in a two-spin Heisenberg XXX system. The x-direction of Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) and Dzyaloshinskii–Moriya (DM) interactions as well as the intrinsic decoherence are considered. We show that the interactions are responsible of transforming separable states to correlated states. We point out that by strengthening the two-spin antiferromagnetic interaction coupling, it is possible to increase the capacity to develop semi-regularly maximal two-spin correlations. By increasing the DM and KSEA x-components, the two-spin XXX–Heisenberg exalts maximal local Fisher information and concurrence correlations with large amplitudes and high frequencies. As the intrinsic decoherence increases, the amplitudes and frequencies of the correlations decrease, which also causes the phenomena of sudden death–birth and sudden changes of the correlations. The two-spin correlation produced by the unitary x-component interactions can be shielded from the intrinsic decoherence by increasing the two-spin antiferromagnetic interaction coupling.
We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii—Moriya (DM) interaction. We find that the effects of DM interaction on antiferromagnetic system is distinct from that of ferromagnetic system. The magnetic field supplemented with DM term contribute to enhance the range of quantum discord. It is revealed that the situations where quantum discord fails to indicate a sudden change of groundstate at finite temperature though indicating such a sudden change of groundstate at zero temperature. Dynamics of pairwise thermal quantum discord is considered as well. Thermal quantum discord vanishes in asymptotic limit regardless of its initial values, however, thermal entanglement suddenly disappears in finite time.
In this paper, we study the thermal dynamics of quantum correlations and uncertainty relation in a three-qubit spin chain under the effect of Hamiltonian XY model, Dzyaloshinskii–Moriya (DM) interaction and external magnetic field. The results show that quantum correlations behave contrary to uncertainty under the effect of thermal dynamics and external magnetic field. However, they evolve in the same way under effect of DM interaction and spin coupling. DM interaction, magnetic field and spin coupling enhance quantum correlations.