  In this paper, we study the Loschmidt Echo (LE) of a two-dimensional Kitaev
model residing on a honeycomb lattice which is chosen to be an environment that
is coupled globally to a central spin. The decay of LE is highly influenced by
the quantum criticality of the environmental spin model e.g., it shows a sharp
dip close to the anisotropic quantum critical point (AQCP) of its phase
diagram. The early time decay and the collapse and revival as a function of
time at AQCP do also exhibit interesting scaling behavior with the system size
which is verified numerically. It has also been observed that the LE stays
vanishingly small throughout the gapless phase of the model. The above study
has also been extended to the 1D Kitaev model i.e. when one of the interaction
terms vanishes.
