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The quantum coherence of the two-site XYZ model with Dzyaloshinsky-Moriya(DM) interactions in an external inhomogenous magnetic field is studied. The DMinteraction, the magnetic field and the measurement basis can be alongdifferent directions, and we examine the quantum coherence at finitetemperature. With respect to the spin-spin interaction parameter, we find thatthe quantum coherence decreases when the direction of measurement basis is thesame as that of the spin-spin interaction. When the spin-lattice interaction isvaried, the coherence always increases irrespective of the relation between itsdirection and the measurement basis. Similar analysis of quantum coherencebased on the variation of the external inhomogenous magnetic field is alsocarried out, where we find that the coherence decreases when the direction ofthe measurement basis is the same as that of the external field.

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