  We study the temporal evolution of the circuit complexity after the local
quench where two harmonic chains are suddenly joined, choosing the initial
state as the reference state. We discuss numerical results for the complexity
for the entire chain and the subsystem complexity for a block of consecutive
sites, obtained by exploiting the Fisher information geometry of the covariance
matrices. The qualitative behaviour of the temporal evolutions of the subsystem
complexity depends on whether the joining point is inside the subsystem. The
revivals and a logarithmic growth observed during these temporal evolutions are
discussed. When the joining point is outside the subsystem, the temporal
evolutions of the subsystem complexity and of the corresponding entanglement
entropy are qualitatively similar.
