Scattering of charge and spin excitations and equilibration of a one-dimensional Wigner crystal

TL;DR

This paper investigates how charge and spin excitations in a one-dimensional Wigner crystal scatter and equilibrate, revealing that spin excitation scattering primarily drives the system's equilibration and affecting quantum wire conductance.

Contribution

The study introduces leading corrections to the integrable model of a 1D Wigner crystal, including charge-spin coupling and next-nearest neighbor exchange, to explain excitation scattering and equilibration.

Findings

Spin excitation scattering dominates equilibration rate

Charge-spin coupling influences excitation dynamics

Results impact understanding of quantum wire conductance

Abstract

We study scattering of charge and spin excitations in a system of interacting electrons in one dimension. At low densities electrons form a one-dimensional Wigner crystal. To first approximation the charge excitations are the phonons in the Wigner crystal, and the spin excitations are described by the Heisenberg model with nearest neighbor exchange coupling. This model is integrable and thus incapable of describing some important phenomena, such as scattering of excitations off each other and the resulting equilibration of the system. We obtain the leading corrections to this model, including charge-spin coupling and the next-nearest neighbor exchange in the spin subsystem. We apply the results to the problem of equilibration of the one-dimensional Wigner crystal and find that the leading contribution to the equilibration rate arises from scattering of spin excitations off each other. We discuss the implications of our results for the conductance of quantum wires at low electron densities.