On the possibility of complete revivals after quantum quenches to a critical point

In a recent letter, J. Cardy, Phys. Rev. Lett. \textbf{112}, 220401 (2014), the author made a very interesting observation that complete revivals of quantum states after quantum quench can happen in a period which is a fraction of the system size. This is possible for critical systems that can be described by minimal conformal field theories (CFT) with central charge $c<1$. In this article, we show that these complete revivals are impossible in microscopic realizations of those minimal models. We will prove the absence of the mentioned complete revivals for the critical transverse field Ising chain analytically, and present numerical results for the critical line of the XY chain. In particular, for the considered initial states, we will show that criticality has no significant effect in partial revivals. We also comment on the applicability of quasi-particle picture to determine the period of the partial revivals qualitatively. In particular, we detect a regime in the phase diagram of the XY chain which one can not determine the period of the partial revivals using the quasi-particle picture.