A Wigner molecule at extremely low densities: a numerically exact study
arXiv:1907.02421 · doi:10.21468/SciPostPhysCore.1.1.001
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.
arXiv commentResubmission to SciPost 8 pages, 3 figures
References in corpus (19)
- Electron Localization in the Insulating State
- Polarization and localization in insulators: generating function approach
- Crossover from Fermi liquid to Wigner molecule behavior in quantum dots
- Electron localization in the insulating state: application to crystalline semiconductors
- Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube
- Strong correlation in Kohn-Sham density functional theory
- Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
- New measure of electron correlation
- Reference electronic structure calculations in one dimension
- Momentum distribution of the uniform electron gas: improved parametrization and exact limits of the cumulant expansion
- Exact wave functions of two-electron quantum rings
- Electron Localization in the Quantum-Hall Regime
- Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
- Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking
- Natural occupation numbers: When do they vanish?
- Uniform electron gases. I. Electrons on a ring
- A simple position operator for periodic systems
- Temperature-induced emergence of Wigner correlations in a STM-probed one-dimensional quantum dot
- Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension
Cited by in corpus (6)
- Accurate ground-state energies of Wigner crystals from a simple real-space approach
- Wigner localization in two and three dimensions: an \emph{ab initio} approach
- A unique one-body position operator for periodic systems
- The localization spread and polarizability of rings and periodic chains
- The Wigner localization of interacting electrons in a one-dimensional harmonic potential
- Artificial versus Natural Atoms: The uncanny capability of the many-body Schrödinger equation to produce emergent behavior