  We investigate the dynamics following sudden quenches across quantum critical
points belonging to different universality classes. Specifically, we use matrix
product state methods to study the quantum Ising chain in the presence of two
additional terms which break integrability. We find that in all models the rate
function for the return probability to the initial state becomes a non-analytic
function of time in the thermodynamic limit. This so-called `dynamical phase
transition' was first observed in a recent work by Heyl, Polkovnikov, and
Kehrein [Phys. Rev. Lett. 110, 135704 (2013)] for the exactly-solvable quantum
Ising chain, which can be mapped to free fermions. Our results for `interacting
theories' indicate that non-analytic dynamics is a generic feature of sudden
quenches across quantum critical points. We discuss potential connections to
the dynamics of the order parameter.
