Entanglement in the anisotropic Heisenberg XYZ model with different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic field

We investigate the entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii-Moriya (DM) interaction and inhomogeneous magnetic field. It is found that the control parameters (Dx, Bx and bx) are remarkably different with the common control parameters (Dz, Bz and bz) in the entanglement and the critical temperature, and these x-component parameters can increase the entanglement and the critical temperature more efficiently. Furthermore, we show the properties of these x-component parameters for the control of entanglement. In the ground state, increasing Dx (spin-orbit coupling parameter) can decrease the critical value bxc and increase the entanglement in the revival region, and adjusting some parameters (increasing bx and J, decreasing Bx and Δ) can decrease the critical value Dxc to enlarge the revival region. In the thermal state, increasing Dx can increase the revival region and the entanglement in the revival region (for T or bx), and enhance the critical value Bxc to make the region of high entanglement larger. Also, the entanglement and the revival region will increase with the decrease of Bx (uniform magnetic field). In addition, small bx (nonuniform magnetic field) has some similar properties to Dx, and with the increase of bx the entanglement also has a revival phenomenon, so that the entanglement can exist at higher temperature for larger bx.