Quantum Quench dynamics in Non-local Luttinger Model: Rigorous Results

TL;DR

This paper rigorously analyzes the dynamics of a non-local Luttinger model after a quantum quench, revealing moving density peaks and a decaying quasi-particle weight using advanced mathematical methods.

Contribution

It provides the first rigorous proof of the time evolution and quasi-particle behavior in a non-local Luttinger model after a quantum quench.

Findings

Density exhibits two peaks moving in opposite directions with renormalized velocity.

A Landau quasi-particle weight appears and vanishes over time.

Results are established using Mattis-Lieb diagonalization and Bosonization methods.

Abstract

We investigate, in the Luttinger model with fixed box potential, the time evolution of an inhomogeneous state prepared as a localized fermion added to the noninteracting ground state. We proved that, if the state is evolved with the interacting Hamiltonian, the averaged density has two peaks moving in opposite directions, with a constant but renormalized velocity. We also proved that a dynamical `Landau quasi-particle weight' appears in the oscillating part of the averaged density, asymptotically vanishing with large time. The results are proved with the Mattis-Lieb diagonalization method. A simpler proof with the exact Bosonization formulas is also provided.