We study the non-equilibrium 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 non-linear 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 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 generalised 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.
In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.