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

We study a particular type of local quench in a generic quantum critical one-dimensional system, using conformal field theory (CFT) techniques, and providing numerical checks of the results in free fermion systems. The system is initially cut into two subsystems A and B which are glued together at time t = 0. We study the entropy of entanglement (EE) between the two parts A and B, using previous results obtained by Calabrese and Cardy (2004 J. Stat. Mech. P06002; 2007 J. Stat. Mech. P10004), and further extending them. We also study in detail the (logarithmic) Loschmidt echo (LLE). For finite size systems both quantities turn out to be (almost) periodic in the scaling limit, and exhibit striking light-cone effects. While these two quantities behave similarly immediately after the quench-namely as c/3log t for the EE and c/4log t for the LLE-we observe some discrepancy once the excitations emitted by the quench bounce on the boundary and evolve within the same subsystem A (or B). The decay of the EE is then non-universal, as noticed by Eisler and Peschel (2007 J. Stat. Mech. P06005). In contrast, we find that the evolution of the 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 these light-cone effects, we also introduce a variant of the Loschmidt echo specifically constructed to detect the excitations emitted just after the quench.