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We study a particular type of local quench in a generic quantum criticalone-dimensional system, using conformal field theory (CFT) techniques, andproviding numerical checks of the results in free fermion systems. The systemis initially cut into two subsystems $A$ and $B$ which are glued together attime $t=0$. We study the entanglement entropy (EE) between the two parts $A$and $B$, using previous results by Calabrese and Cardy, and further extendingthem. We also study in detail the (logarithmic) Loschmidt echo (LLE). Forfinite-size systems both quantities turn out to be (almost) periodic in thescaling limit, and exhibit striking light-cone effects. While these twoquantities behave similarly immediately after the quench---namely as $c/3 \logt$ for the EE and $c/4 \log t$ for the LLE---, we observe some discrepancy oncethe excitations emitted by the quench bounce on the boundary and evolve withinthe same subsystem $A$ (or $B$). The decay of the EE is then non-universal, asnoticed by Eisler and Peschel. On the contrary, we find that the evolution ofthe LLE is less sensitive than the EE to non-universal details of the model,and is still accurately described by our CFT prediction. To further probe theselight-cone effects, we also introduce a variant of the Loschmidt echospecifically constructed to detect the excitations emitted just after thequench.

Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects