Quantum Quench for inhomogeneous states in the non-local Luttinger model

TL;DR

This paper analytically studies the time evolution of inhomogeneous states in a non-local Luttinger model, revealing variable peak velocities and a decaying Landau quasi-particle weight over time.

Contribution

It provides an exact analytical analysis of inhomogeneous state dynamics in a non-local Luttinger model, highlighting novel velocity variations and quasi-particle decay effects.

Findings

Peaks in density move with variable velocities

Landau quasi-particle weight diminishes over time

Fermions are not excitations of the interacting Hamiltonian

Abstract

In the Luttinger model with non-local interaction we investigate, by exact analytical methods, the time evolution of an inhomogeneous state with a localized fermion added to the non interacting ground state. In absence of interaction the averaged density has two peaks moving in opposite directions with constant velocities. If the state is evolved with the interacting Hamiltonian two main effects appear. The first is that the peaks have velocities which are not constant but vary between a minimal and maximal value. The second is that a dynamical `Landau quasi-particle weight' appears in the oscillating part of the averaged density, asymptotically vanishing with time, as consequence of the fact that fermions are not excitations of the interacting Hamiltonian.