Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain

We consider time evolution of order parameters and entanglement asymmetries in the ferromagnetic phase of the transverse-field Ising chain. One side of the system is prepared in a ferromagnetic ground state and the other side either in equilibrium at higher temperature or out of equilibrium. We focus on the disorder-order interface in which the order parameter attains a nonzero value, different from the ground state one. In that region, correlations follow a universal behaviour. We analytically compute the asymptotic scaling functions of the one- and two-point equal time correlations of the order parameter and provide numerical evidence that also the non-equal time correlations are universal. We analyze the R\'enyi entanglement asymmetries of subsystems and obtain a prediction that is expected to hold also in the von Neumann limit. Finally, we show that the Wigner-Yanase skew information of the order paramerter in subsystems within the interfacial region scales as their length squared. We propose a semiclassical approximation that is particularly effective close to the edge of the lightcone.