Narrow Results

In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii–Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators ${Ŝ}_x,{Ŝ}_y$ and ${Ŝ}_z$ in the matrix forms with the introduction of bilinear exchange interaction ($J_{\mu }$), the Dzyaloshinskii–Moriya interaction (DMI) (${\mathrm{\Delta }}_{\mu }$) and external magnetic fields ($H_{\mu }$) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations $M_{\mu }^A$ and $M_{\mu }^B$ are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers $q=3,4$ and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all ${\mathrm{\Delta }}_{\mu }\ne 0.0$, between FM and AFM when ${\mathrm{\Delta }}_{\mu }=0.0$ only and, AFM and R at low temperatures for very small ${\mathrm{\Delta }}_{\mu }$ and $H_{\mu }$ values.