Quantum quench in 1D: Coherent inhomogeneity amplification and 'supersolitons'

TL;DR

This paper investigates how a quantum quench in a 1D system causes inhomogeneities to be amplified over time, leading to unbounded growth of density waves, with implications for understanding non-equilibrium dynamics in Luttinger liquids.

Contribution

It demonstrates power law amplification of density inhomogeneities post-quench and links the scaling to fractionalization in Luttinger liquids.

Findings

Density inhomogeneities grow as a power law over time.

Traveling density waves increase in amplitude without bound.

Amplification is governed by the fractionalization of quasiparticles.

Abstract

We study a quantum quench in a 1D system possessing Luttinger liquid (LL) and Mott insulating ground states before and after the quench, respectively. We show that the quench induces power law amplification in time of any particle density inhomogeneity in the initial LL ground state. The scaling exponent is set by the fractionalization of the LL quasiparticle number relative to the insulator. As an illustration, we consider the traveling density waves launched from an initial localized density bump. While these waves exhibit a particular rigid shape, their amplitudes grow without bound.