Failure of standard approximations of the exchange coupling in nanostructures

TL;DR

This paper introduces a numerically exact finite-element method to calculate exchange coupling in quantum dot systems, revealing that standard approximation schemes lack reliable predictive accuracy for real nanostructures.

Contribution

The authors develop a novel, efficient numerical technique that accurately computes exchange coupling, challenging the reliability of traditional approximation methods in quantum dot modeling.

Findings

Standard approximations often fail to predict exchange coupling accurately.

Numerical results show significant deviations from traditional methods.

The new method provides a more reliable tool for quantum dot analysis.

Abstract

We calculate the exchange coupling for a double dot system using a novel, numerically exact yet efficient technique, based on finite-element methods. Specifically, we evaluate the exchange coupling both for a quasi-one and a two-dimensional system, also including an applied magnetic field. Our numerical results provide a stringent test for standard approximation schemes (e.g., Heitler-London, Hund-Mulliken, Hubbard), and they show that the standard methods do not have reliable predictive power for real quantum-dot systems.