Solitons in a one-dimensional Wigner crystal

TL;DR

This paper explores the existence of solitons as elementary excitations in a one-dimensional Wigner crystal, revealing new modes beyond phonons and analyzing their spectral properties and stability.

Contribution

It introduces the concept of solitons in a 1D Wigner crystal and computes their excitation spectrum, highlighting their potential stability at low energies.

Findings

Solitons are supported as elementary excitations alongside phonons.

Solitons exhibit a parametrically small decay rate at low energies.

Implications for the dynamic structure factor are discussed.

Abstract

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. We compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. We discuss implications of our results for the behavior of the dynamic structure factor.