  We study the complete phase space and the quench dynamics of an exactly
solvable spin chain, the cluster-XY model. In this chain, the cluster term and
the XY couplings compete to give a rich phase diagram. The phase diagram is
studied by means of the quantum geometric tensor. We study the time evolution
of the system after a critical quantum quench using the Loschmidt echo. The
structure of the revivals after critical quantum quenches presents a non
trivial behavior depending on the phase of the initial state and the critical
point.
