Sudden transitions of trace distance discord of dipole-dipole coupled two qubits

We investigate the exact dynamics of trace distance discord by considering two qubits under dephasing whose states belong to a class of $X$ states beyond Bell diagonal form. The necessary condition for the occurrence of freezing trace distance discord is found and compared with that of entropic discord. For an illustration, we consider two interacting qubits coupled to independent reservoirs and demonstrate these dynamical properties of trace distance discord. It is interesting to find that the freezing trace distance discord exists even for $X$ states without maximally mixed marginals and can be tuned by dipole-dipole coupling of two qubits. Moreover, we consider the initial extended Werner-like states and investigate the differences between trace distance discord and entanglement. The influences of initial state and the dipole-dipole coupling of the two qubits on the dynamics of nonclassical correlations are explored.