Luttinger liquid universality in the time evolution after an interaction quench

TL;DR

This paper demonstrates that the long-time relaxation dynamics of one-dimensional Fermi systems after an interaction quench exhibit universal behavior characterized by Luttinger liquid parameters, confirmed through analytical and numerical methods.

Contribution

It provides analytical expressions for universal functions governing relaxation and verifies universality in lattice fermions using DMRG, extending Luttinger liquid theory to non-equilibrium dynamics.

Findings

Universal long-time behavior described by Luttinger parameters

Analytical derivation for the Tomonaga-Luttinger model

Numerical verification with density matrix renormalization group

Abstract

We provide strong evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: The leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density matrix renormalization group.