I will discuss the non-equilibrium dynamics in interacting systems subjected to quantum quenches. In such a process, a system is prepared in the ground state of a given Hamiltonian, we then introduce a sudden change in the system and let it evolves in time according to a new Hamiltonian. In the talk, I will introduce this subject and then exemplify it with results obtained in my group. 

In a first case [1], we connect two spin-1/2 XXZ chains prepared in different phases, one in the ferromagnetic phase and the other in the critical (Luttinger) phase. We show that the on-site magnetization and bipartite entanglement entropy follow effective light cones after the quench, which are determined by different types of excitations depending on the system parameters.

In a second case [2], a magnetic impurity is suddenly coupled to interacting chains. We find that the local magnetization at the impurity site decays faster if we increase the electronic interaction in the chains, even though the spin velocity decreases. At intermediate timescales, we obtain insights into the time evolution of the Kondo screening cloud in interacting systems.

[1] A. L. de Paula et al., Physical Review B 95, 045125 (2017).
[2] Helena Bragança et al., Physical Review B 103, 125152 (2021).