We first provide a formula to calculate the probability of occurrence of different configurations (formation probabilities) in a generic free fermion system. We then study the scaling of these probabilities with respect to the size in the case of critical transverse-field XY-chain in the σ z bases. In the case of the transverse field Ising model, we show that all the "crystal" configurations follow the formulas expected from conformal field theory (CFT). In the case of critical XX chain, we show that the only configurations that follow the formulas of the CFT are the ones which respect the filling factor of the system. By repeating all the calculations in the presence of open and periodic boundary conditions we find further support to our classification of different configurations. Using the developed technique, we also study Shannon information of a subregion in our system. In this respect we distinguish particular configurations that are more important in the study of the scaling limit of the Shannon information of the subsystem. Finally, we study the evolution of formation probabilities, Shannon information and Shannon mutual information after a quantum quench in free fermion system. In particular, for the intial state considered in this paper, we demonstrate that the Shannon information after quantum quench first increases with the time and then saturates at time, where l is the size of the subsystem.

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We study the light-cone velocity for global quenches in the non-interacting XY chain starting from a class of initial states that are eigenstates of the local z-component of the spin. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread. As a consequence the light-cone velocity can be state-dependent also for non-interacting systems: a new effect of which we provide clear numerical evidence and analytic predictions. Analogous considerations, based on numerical results, are drawn for the evolution of the entanglement entropy. arXiv:1803.03856v2 [cond-mat.str-el] 3 May 2018