Thermal coherence of the Heisenberg model with Dzyaloshinsky-Moriya interactions in an inhomogenous external field

The quantum coherence of the two-site XYZ model with Dzyaloshinsky-Moriya (DM) interactions in an external inhomogenous magnetic field is studied. The DM interaction, the magnetic field and the measurement basis can be along different directions, and we examine the quantum coherence at finite temperature. With respect to the spin-spin interaction parameter, we find that the quantum coherence decreases when the direction of measurement basis is the same as that of the spin-spin interaction. When the spin-lattice interaction is varied, the coherence always increases irrespective of the relation between its direction and the measurement basis. Similar analysis of quantum coherence based on the variation of the external inhomogenous magnetic field is also carried out, where we find that the coherence decreases when the direction of the measurement basis is the same as that of the external field.