  We investigate the time dynamics of quantum correlations of the anisotropic
Heisenberg model in a time-dependent magnetic field, in one-dimensional,
ladder, and two-dimensional lattices. We find that quantum correlation measures
in the entanglement-separability paradigm are ergodic in these systems
irrespective of system parameters. However, information-theoretic quantum
correlation measures can also be nonergodic, and exhibit a transition from
nonergodic to ergodic behavior with the change of interaction strength in the
direction of the magnetic field. We also observe that the transition point
changes drastically as we go from one-dimensional and ladder lattices to the
two-dimensional one.
