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

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.

References in corpus (6)

• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• Energy relaxation and thermalization of hot electrons in quantum wires
• Spin coupling in zigzag Wigner crystals
• Equilibration of a one-dimensional Wigner crystal
• Coulomb drag between ballistic quantum wires
• Kondo polarons in a one-dimensional Fermi gas

Cited by in corpus (7)

• Wigner Crystals in Two-Dimensional Transition-Metal Dichalcogenides: Spin Physics and Readout
• Thermal Transport in One Dimensional Electronic Fluid
• Second sound in systems of one-dimensional fermions
• Interaction-induced backscattering in short quantum wires
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Kinetic processes in Fermi-Luttinger liquids
• Brownian scattering of a spinon in a Luttinger liquid