Short-range interactions in a two-electron system: energy levels and magnetic properties

TL;DR

This study investigates how short-range Yukawa interactions influence energy levels and magnetic properties of a two-electron system in a square billiard under a magnetic field, revealing suppression of Wigner molecules and complex susceptibility behavior.

Contribution

It provides a detailed analysis of energy spectra and magnetic responses considering finite-range interactions, highlighting effects on Wigner molecule formation and susceptibility oscillations.

Findings

Short-range interactions suppress Wigner molecule formation.

Magnetic susceptibility exhibits paramagnetic peaks due to exchange oscillations.

Interaction effects lead to paramagnetic and diamagnetic phases depending on temperature.

Abstract

The problem of two electrons in a square billiard interacting via a finite-range repulsive Yukawa potential and subjected to a constant magnetic field is considered. We compute the energy spectrum for both singlet and triplet states, and for all symmetry classes, as a function of the strength and range of the interaction and of the magnetic field. We show that the short-range nature of the potential suppresses the formation of ``Wigner molecule'' states for the ground state, even in the strong interaction limit. The magnetic susceptibility $\chi(B)$ shows low-temperature paramagnetic peaks due to exchange induced singlet-triplet oscillations. The position, number and intensity of these peaks depend on the range and strength of the interaction. The contribution of the interaction to the susceptibility displays paramagnetic and diamagnetic phases as a function of $T$.