  The experimental realization of lattices with Chern bands in ultracold-atom
and photonic systems has motivated the study of time-dependent phenomena, such
as spatial propagation, in lattices with nontrivial topology. We study the
dynamics of gaussian wavepackets on the Haldane honeycomb Chern-band lattice
model, in the presence of a harmonic trap. We focus on the transverse response
to a force, which is due partly to the Berry curvature and partly to the
transverse component of the energy band curvature. We evaluate the accuracy of
a semiclassical description, which treats the wavepacket as a point particle in
both real and momentum space, in reproducing the motion of a realistic
wavepacket with finite extent. We find that, in order to accurately capture the
wavepacket dynamics, the extent of the wavepacket in momentum space needs to be
taken into account. The dynamics is sensitive to the interplay of band
dispersion and Berry curvature over the finite region of momentum (reciprocal)
space where the wavepacket has support. Moreover, if the wavepacket is prepared
with a finite initial momentum, the semiclassical analysis reproduces its
motion as long as it has a large overlap with the eigenstates of a single band.
The semiclassical description generally improves with increasing real-space
size of the wavepacket, as long as the external conditions (e.g., external
force) remain uniform throughout the spatial extent of the wavepacket.
