  We investigate the propagation of a local perturbation in the two-dimensional
transverse-field Ising model with a time-dependent application of mean-field
theory based on the BBGKY hierarchy. We show that the perturbation propagates
through the system with a finite velocity and that there is transition from
Manhattan to Euclidian metric, resulting in a light cone with an almost
circular shape at sufficiently large distances. The propagation velocity of the
perturbation defining the front of the light cone is discussed with respect to
the parameters of the Hamiltonian and compared to exact results for the
transverse-field Ising model in one dimension.

Quantum Physics;Statistical Mechanics