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