Quantum quench dynamics of the Coulomb Luttinger model

We study the nonequilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex correlations, its finite time dynamics, and the stationary state limit. Correlations exhibit a nonlinear light-cone effect: The spreading of the initial signal accelerates as a consequence of the quantum nature of the excitations, whose peculiar dispersion of plasmonic type in one dimension (1D) gives rise to a logarithmic divergence in the group velocity at q = 0. In addition, we show that both the static and dynamic stationary state correlations can be reproduced with a simple generalized Gibbs ensemble despite the long-range character of the interactions which precludes the application of the Lieb-Robinson bounds. We propose a suitable experimental setup in which these effect can be observed based on ultracold ions loaded on linear traps.