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

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Computational Physics

Background:

• Understanding electron behavior at low densities is crucial for developing new materials and quantum technologies.
• Wigner localization describes a state where electrons form a crystal lattice due to strong interactions, a phenomenon predicted but challenging to observe.
• Previous methods struggled to accurately model electron wave functions at extremely low densities.

Purpose of the Study:

• To investigate and confirm Wigner localization in two interacting electrons at very low densities.
• To develop and validate a computational method capable of accurately describing electronic wave functions in this regime.
• To explore Wigner localization in both two and three dimensions.

Main Methods:

• Exact diagonalization of the many-body Hamiltonian.
• Utilizing a novel method with Clifford periodic boundary conditions and a renormalized Coulomb potential.
• Employing Gaussian-type orbitals for accurate electronic wave function representation and exploiting translational symmetry for computational efficiency.

Main Results:

• Successfully observed Wigner localization without ambiguity in simulations.
• Accurately described the electronic wave function even at very low electron densities.
• Validated the computational approach by comparing results with a known semi-classical model.

Conclusions:

• The developed computational method reliably captures Wigner localization at low electron densities.
• The study provides accurate insights into electron correlation and localization phenomena.
• This work advances the understanding of quantum many-body systems and their behavior in reduced dimensions.