Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1907.02421 · SciPost Physics Core

A Wigner molecule at extremely low densities: a numerically exact study

Miguel Escobar Azor, Léa Brooke, Stefano Evangelisti, Thierry Leininger, Pierre‐François Loos, Nicolas Suaud, J. A. Berger

Published Nov 11, 2019• 16 citations
arXivHTMLPDF

Abstract

In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state and it can be applied to systems of all sizes.

DOI
10.21468/scipostphyscore.1.1.001

Related papers

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

Xabier Telleria‐Allika, Miguel Escobar Azor, Grégoire François +5 more

In this work, we study the Wigner localization of interacting electrons that are confined to a quasi-one-dimensional harmonic potential using accurate quantum chemistry 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.

arXiv:2207.12014•The Journal of Chemical Physics•Oct 10, 2022•3 citations

Wigner localization in two and three dimensions: An ab initio approach

Miguel Escobar Azor, Estefania Alves, Stefano Evangelisti +1 more

In this work, we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function, we use a regular distribution in space of Gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach, we are able to observe the Wigner localization without ambiguity.

arXiv:2107.05321•The Journal of Chemical Physics•Sep 28, 2021•12 citations

Quantum Monte Carlo study of few-electron concentric double quantum rings

Leonardo Colletti, Francesc Malet, Martí Pi +1 more

We consider few-electron concentric double quantum rings with parabolic confining potential and compare the ground-state energies calculated by exact diagonalization of the Hamiltonian, accurate quantum Monte Carlo, and local spin-density functional approaches. Electronic localization in one of the rings and the formation of rotating Wigner molecules is shown, respectively, from the one-body and the two-body density operators. As the confinement strength of the outer ring is finely increased, the circularly symmetric electron density exhibits a radial crossover from this ring to the inner one without altering the angular character of the system.

Physical Review B•Mar 17, 2009•14 citations

Interacting electrons on a quantum ring: accuracy and optimization of the Jastrow-Slater wave function for local and nonlocal Hamiltonians

Sigríður Sif Gylfadóttir, Ari Harju, Teppo T. Jouttenus +1 more

We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wave function captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultrathin quantum ring system happens at quite high electron density.

•Nov 3, 2005•0 citations

Signatures of Wigner localization in one-dimensional systems

Alejandro Díaz-Márquez, Stefano Battaglia, Gian Luigi Bendazzoli +3 more

We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.

The Journal of Chemical Physics•Mar 22, 2018•27 citations

Interacting electrons on a quantum ring: exact and variational approach

S S Gylfadottir, Ari Harju, Teppo T. Jouttenus +1 more

We study a system of interacting electrons on a one-dimensional (1D) quantum ring using exact diagonalization (ED) and the variational quantum Monte Carlo (VMC) method. We examine the accuracy of the Slater–Jastrow-type many-body wavefunction and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wavefunction captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultra-thin quantum ring system happens at quite high electron density.

arXiv:cond-mat/0511075•New Journal of Physics•Sep 27, 2006•16 citations
In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state and it can be applied to systems of all sizes.
In this work, we study the Wigner localization of interacting electrons that are confined to a quasi-one-dimensional harmonic potential using accurate quantum chemistry 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.
In this work, we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function, we use a regular distribution in space of Gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach, we are able to observe the Wigner localization without ambiguity.
We consider few-electron concentric double quantum rings with parabolic confining potential and compare the ground-state energies calculated by exact diagonalization of the Hamiltonian, accurate quantum Monte Carlo, and local spin-density functional approaches. Electronic localization in one of the rings and the formation of rotating Wigner molecules is shown, respectively, from the one-body and the two-body density operators. As the confinement strength of the outer ring is finely increased, the circularly symmetric electron density exhibits a radial crossover from this ring to the inner one without altering the angular character of the system.
We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wave function captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultrathin quantum ring system happens at quite high electron density.
We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.
We study a system of interacting electrons on a one-dimensional (1D) quantum ring using exact diagonalization (ED) and the variational quantum Monte Carlo (VMC) method. We examine the accuracy of the Slater–Jastrow-type many-body wavefunction and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wavefunction captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultra-thin quantum ring system happens at quite high electron density.