Interplay between short-range and critical long-range fluctuations in the out-of-equilibrium behavior of the particle density at quantum transitions

We address the equilibrium and out-of-equilibrium behavior of the particle density in many-body systems undergoing quantum transitions driven by the chemical potential mu. They originate from a nontrivial interplay between noncritical short-range and critical long-range quantum fluctuations. As a paradigmatic model, we consider the one-dimensional fermionic Kitaev model, for which very accurate numerical studies can be performed, up to O(104) chain sites. The search for dynamic scaling behaviors of the particle density is complicated by the fact that its equilibrium (ground-state) behavior is dominated by short-range fluctuations, giving rise to regular background terms and peculiar logarithmic terms from resonances between renormalization-group perturbations associated with the energy and identity operator families within the conformal field theory. To study these issues, we focus on two dynamic protocols, either instantaneous quenches or quasiadiabatic changes of mu, to the critical value mu c, unveiling out-of-equilibrium scaling behaviors of the particle density, which arise from the critical modes, within a dynamic finite-size scaling framework.