Local quantum Fisher information and local quantum uncertainty for general X-states

A two-spin-1/2 Heisenberg XYZ model with Dzyaloshinsky–Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions in the presence of an inhomogeneous external magnetic field is considered at thermal equilibrium. Its density matrix has the general X form for which we derive explicit formulas for the local quantum Fisher information (LQFI) and local quantum uncertainty (LQU) directly in terms of model parameters. This allows us to perform a comparative study for the discord-type quantum correlations LQFI and LQU and to reveal a number of new features in their behavior. In particular, the sudden transitions of quantum correlations with a smooth change in temperature are found. Moreover, it is shown that there may be a sequence of such transitions for certain choices of interaction constants.