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.
Highlights
We have investigated Wigner localization at extremely low densities using an exact diagonalization of the many-body Hamiltonian for a system of two electrons confined to a ring
Due to the rotational symmetry of the system, Wigner localization cannot be observed in the local density
With respect to the two-body reduced density matrix, the advantage of the localization tensor is that it can be applied without increased difficulty to systems with more dimensions and more electrons
Summary
When studying a system constituted of only electrons, one can consider two limiting regimes, that of high and low density. [13,14,15] Instead, in this work we use the exact diagonalization of the many-body Hamiltonian to obtain numerically exact results This allows us to explore the regime of extremely low densities, down to densities of the order of 1 electron per 10 μm. We used a multi-purpose software for the numerical calculations due to which we were limited to system sizes smaller than 100 Bohr Due to these restrictions we were not able to fully appreciate the delta-peak nature of the Wigner localization in the many-body wave function. We will limit our study to two electrons, since it is sufficient to observe the Wigner localization while at the same time it allows us to obtain numerically exact results by exact diagonalization of the Hamiltonian.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
