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We study the complete phase space and the quench dynamics of an exactlysolvable spin chain, the cluster-XY model. In this chain, the cluster term andthe XY couplings compete to give a rich phase diagram. The phase diagram isstudied by means of the quantum geometric tensor. We study the time evolutionof the system after a critical quantum quench using the Loschmidt echo. Thestructure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the criticalpoint.

Phase diagram and quench dynamics of the Cluster-XY spin chain