Exchange Coupling in a One-Dimensional Wigner Crystal

TL;DR

This paper investigates the exchange coupling in a one-dimensional Wigner crystal formed in a low-density quantum wire, focusing on the exponential dependence of the coupling constant J due to electron tunneling.

Contribution

It provides a detailed analysis of how many-body effects and wire width influence the exponential behavior of exchange coupling in a 1D Wigner crystal.

Findings

Exchange coupling J is exponentially small at low densities.

Many-body effects significantly affect the tunneling process.

Finite wire width modifies the coupling strength.

Abstract

We consider a long quantum wire at low electron densities. In this strong interaction regime a Wigner crystal may form, in which electrons comprise an antiferromagnetic Heisenberg spin chain. The coupling constant J is exponentially small, as it originates from tunneling of two neighboring electrons through the segregating potential barrier. We study this exponential dependence, properly accounting for the many-body effects and the finite width of the wire.