Light-cone like spreading of correlations in the Bose Hubbard model at strong coupling

We study the spreading of correlations in space and time after a quantum quench in the Bose Hubbard model. We derive equations of motion for the single-particle Green's function within the contour-time formalism, allowing us to study dynamics in the strong coupling regime. We discuss the numerical solutions of these equations and calculate the single-particle density matrix for quenches in the Mott phase. We demonstrate light-cone like spreading of correlations in the Mott phase in one, two, and three dimensions and calculate propagation velocities in each dimension. Our results show excellent agreement with existing results in one dimension and demonstrate the anisotropic spreading of correlations in higher dimensions.