  The notion of a dynamical quantum phase transition (DQPT) was recently
introduced in [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the
non-analytic behavior of the Loschmidt echo at critical times in the
thermodynamic limit. In this work the quench dynamics in the ground state
sector of the two-dimensional Kitaev honeycomb model are studied regarding the
occurrence of DQPTs. For general two-dimensional systems of BCS-type it is
demonstrated how the zeros of the Loschmidt echo coalesce to areas in the
thermodynamic limit, implying that DQPTs occur as discontinuities in the second
derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a
phase boundary or within the massless phase. In the 1d limit of the Kitaev
honeycomb model it becomes clear that the discontinuity in the higher
derivative is intimately related to the higher dimensionality of the
non-degenerate model. Moreover, there is a strong connection between the
stationary value of the rate function of the Loschmidt echo after long times
and the occurrence of DQPTs in this model.
