Quantum quench dynamics of the Coulomb Luttinger model

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.

Time evolution during and after finite-time quantum quenches in Luttinger liquids

“…Of course, considering very non-monotonic time dependencies ofĝ 4 (0, t) may lead to a shrinking of the range of momenta over which (25) is applicable.…”

“…A for a more detailed discussion). Apart from the restriction on q the expansions (25) and (26) are valid for quench protocols with arbitrary time dependencies and final interaction strengths g 2/4 (0, τ ). In particular, they are applicable in the non-perturbative regime 1 ĝ 2/4 (0, τ ).…”

“…In particular, they are applicable in the non-perturbative regime 1 ĝ 2/4 (0, τ ). It is straightforward to explicitly verify (25) and (26) for the exactly solvable protocols discussed in Sec. IV [but also the perturbative solution of (22) presented for completeness in App.…”

“…The integral in (D2) is dominated by small momenta q q c , for which we can use the expansions (32) and (33). The additional requirement q 1/(v F τ ) originating from (25) and (26) will be automatically satisfied provided v F q c τ 1, implying that the results are valid for quenches with short to moderate quench times. Writing A(q) = −iA 1 q and B(q) = iB 0 with A 1 , B 0 ∈ R we obtaiñ Finally, expanding the single-mode energy to leading order, (q) = vq + .…”

Prethermalization and thermalization of a quenched interacting Luttinger liquid

“…Initially, the dynamics of local observables at transient and intermediate time scales are controlled by the corresponding integrable theory serving as a metastable attractor for the non-integrable dynamics [4,27,28]. This trapping in a metastable state has been termed prethermalization [27,29] and is expected to exist for several non-integrable models and models close to integrability [4,27,[30][31][32][33][34][35][36][37][38]. In the quasi-particle picture, prethermalization is associated with the initial formation of well-defined excitations [27] which leads to a dephasing of all terms that are not diagonal in quasi-particle modes, i.e.…”