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

TL;DR

This paper analyzes the dynamics of Luttinger liquids during and after finite-time quantum quenches, providing exact solutions and revealing delayed light-cone effects and universal Green function behavior.

Contribution

It offers the first exact, non-perturbative analysis of finite-time quenches in Luttinger liquids, including analytic expressions for delays in propagating fronts.

Findings

Delayed light-cone propagation compared to sudden quenches

Universal behavior of Green functions during quenches

Analytic results for energy and Green function dynamics

Abstract

We consider finite-time quantum quenches in the interacting Tomonaga--Luttinger model, for example time-dependent changes of the nearest-neighbour interactions for spinless fermions. We use the exact solutions for specific protocols including the linear and cosine ramps (or, more generally, periodic pumping). We study the dynamics of the total and kinetic energy as well as the Green functions during as well as after the quench. For the latter we find that the light-cone picture remains applicable, however, the propagating front is delayed as compared to the sudden quench. We extract the universal behaviour of the Green functions and in particular provide analytic, non-perturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.