Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking

Abstract

We address low-density two-dimensional circular quantum dots with spin-restricted Kohn-Sham density functional theory. By using an exchange-correlation functional that encodes the effects of the strongly-correlated regime (and that becomes exact in the limit of infinite correlation), we are able to reproduce characteristic phenomena such as the formation of ring structures in the electronic total density, preserving the fundamental circular symmetry of the system. The observation of this and other well-known effects in Wigner-localized quantum dots such as the flattening of the addition energy spectra, has until now only been within the scope of other, numerically more demanding theoretical approaches. arXiv:1311.6011v2 [cond-mat.str-el]

Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

“…When the confining potential is harmonic, as in the quantum wires and quantum dots studied in Ref. [14][15][16] , the barriers remain finite in the KS SCE potential also at very low density. In LDA we see that at large R H−H there is a barrier localized on the atoms rather than in the midbond, leading to overestimation of the charge in the bond.…”

Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases

“…[52] for a discussion on contact interactions). The SCP functional is thus naturally very well suited for ionic gases in the strong-correlation regime, where it is expected to provide a large part of the total interaction energy [35][36][37]. Even more interesting is the case of general dipolar anisotropic interactions: the SCP functional combined with the KS kinetic energy (fermionic or bosonic) should be able to capture many of the interesting phenomena observed in the strongcorrelation regime [29,53].…”

“…For the Coulomb interaction, this functional has been widely studied [33,39,40], and it has been shown to be able to capture the physics of the strongly-correlated regime in model quantum wires and quantum dots [35][36][37], yielding results beyond the mean-field level. The construction of V SCP int [n] for a given density n(r) is equivalent to an optimal transport (or mass transportation theory, a wellestablished field of mathematics and economics) problem with cost given by the interaction [41,42].…”

“…This provides an effective single-particle potential in a rigorous and physical way [35][36][37] relying on calculations of the uniform system energy by means of other many-body approaches. The formalism becomes asymptotically exact in the limits of both vanishing and extremely strong coupling.…”

“…Our "KS-SCP DFT" approach consists in using V SCP int [n] to approximate the mean-field plus exchange-correlation terms of the total energy functional or, equivalently, its functional derivative v SCP ([n]; r) of Eq. (4) to approximate the Hartree-exchange-correlation potential [36,37],…”