Spin exchange in quantum rings and wires in the Wigner-crystal limit

TL;DR

This paper introduces a precise method to calculate exchange coupling in strongly correlated 1D electron systems, using pair-correlation functions and instanton techniques, with applications to quantum rings.

Contribution

It develops an asymptotically exact approach linking exchange constants to pair-correlation functions, enabling accurate calculations in quantum rings with Coulomb interactions.

Findings

Explicit exchange coupling calculations for quantum rings.

Validation of the instanton approach for strongly correlated electrons.

Enhanced understanding of spin exchange in Wigner-crystal regimes.

Abstract

We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach.