Quantum quench dynamics of the Coulomb Luttinger model

TL;DR

This paper investigates the non-equilibrium dynamics of the Coulomb Luttinger model after sudden interaction changes, revealing a non-linear light cone effect and demonstrating the applicability of a generalized Gibbs ensemble despite long-range interactions.

Contribution

It introduces a detailed analysis of quench dynamics in the Coulomb Luttinger model, highlighting a non-linear light cone effect and the relevance of a generalized Gibbs ensemble.

Findings

Correlations exhibit a non-linear light cone effect.

Stationary state correlations match a generalized Gibbs ensemble.

Long-range interactions do not prevent the ensemble description.

Abstract

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.