Nonmonotonic response and light-cone freezing in fermionic systems under quantum quenches from gapless to gapped or partially gapped states

The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a generalized Gibbs ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, nonmonotonic response of steady-state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the nonmonotonous behavior of observables. In continuum noninteracting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favor of the robustness of the phenomenon in the cases of nonsudden quenches and higher dimensionality.