Adiabatic quenches of quantum critical systems

The last decade saw numerous advances in experimental techniques using cold atomic gases which allow for the highly controlled study of quantum systems and their time evolution. These results triggered a fervent search for an appropriate theoretical description of the dynamics of non-trivial many-body systems. The present work is devoted to this goal.;We focus on the case of one-dimensional Bose gases with repulsive contact interactions. We study two non-equilibrium processes that are realized experimentally: (i) loading a one-dimensional Bose gas into a commensurate optical lattice, and (ii) coupling through tunneling of two identical one-dimensional Bose gases. Both setups can be theoretically described by a time-dependent sine-Gordon model. We analyze this model and consider different quenching protocols of the tuning parameter. We apply adiabatic perturbation theory to describe the scaling behavior of the quantities characterizing the dynamics: the probability of excitations, the number of defects produced during the quench, the excitation energy, and the diagonal entropy. For two specific values of the interaction strength, the hard-core limit, or Tonks-Girardeau regime, and the free bosonic limit, the problem can be solved exactly. We analyze those two exact solutions in detail, also considering their extension to the finite temperature case.;Having analyzed the case of the sine-Gordon model, we extend the analysis to arbitrary systems in d-dimensions that are quenched near a quantum phase transition. We suggest a single framework to study both sudden and slow quenches. We show that the universal scaling of the observables can be connected to the singularities of some static quantities at the critical point. Such quantities are the fidelity susceptibility, in the case of a sudden quench, and generalization of it, in the case of a power-law quench. This connection between dynamics and critical behavior promises to provide insights into the time-evolution of a variety of other quantum systems.