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The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magneticfield with both antisymmetric Dzyaloshinsky-Moriya and symmetricKaplan-Shekhtman-Entin-Wohlman-Aharony cross interactions is considered atthermal equilibrium. Using a group-theoretical approach, we find fifteen spinHamiltonians and as many corresponding Gibbs density matrices (quantum states)whose eigenvalues are expressed only through square radicals. We also foundlocal unitary transformations that connect nine of this fifteen statecollection, and one of them is the X quantum state. Since such quantumcorrelations as quantum entanglement, quantum discord, one-way quantum workdeficit, and others are known for the X state, this allows to get the quantumcorrelations for any member from the nine state family. Further, we show thatthe remaining six quantum states are separable, that they are also connected bylocal unitary transformations, but, however, now the case with knowncorrelations beyond entanglement is generally not available.

On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions