The Wigner localization of interacting electrons in a one-dimensional harmonic potential

TL;DR

This paper investigates the transition to Wigner localization of interacting electrons in a one-dimensional harmonic trap, using a semi-analytical model and electronic-structure properties to identify the localization regime and transition point.

Contribution

It demonstrates that Wigner localization can occur at small confinement parameters and introduces a method to connect localized and delocalized regimes via particle-hole entropy analysis.

Findings

Wigner regime achievable with small confinement parameters

Particle-hole entropy smoothly connects Fermi-gas and Wigner regimes

Maximum entropy indicates the transition point between regimes

Abstract

approaches. We demonstrate that the Wigner regime can be reached using small values of the confinement parameter. To obtain physical insight in our results we analyze them with a semi-analytical model for two electrons. Thanks to electronic-structure properties such as the one-body density and the particle-hole entropy, we are able to define a path that connects the Wigner regime to the Fermi-gas regime by varying the confinement parameter. In particular, we show that the particle-hole entropy as a function of the confinement parameter smoothly connects the two regimes. Moreover, it exhibits a maximum that could be interpreted as the transition point between the localized and delocalized regimes.