Anisotropic quantum dots: Correspondence between quantum and classical Wigner molecules, parity symmetry, and broken-symmetry states

We study electron systems confined in anisotropic quantum dots at high magnetic fields using the configuration-interaction scheme with a multicenter basis of single-electron functions centered around different sites. Elliptical, triangular, and square quantum dots are investigated. We study the relation between the quantum and classical charge density and conclude that at high magnetic field the quantum charge density reproduces all the equivalent lowest-energy configurations of classical point charges. Quantum systems with a classical counterpart of a unique lowest-energy configuration exhibit a smooth convergence of the charge density to the classical limit at high magnetic field. In quantum systems with several equivalent classical configurations the magnetic field induces discontinuous transformations of the ground-state symmetry associated with crossings of the corresponding few-electron energy levels. A linear combination of states with the crossing levels yields a semiclassical charge density with a broken symmetry. At the magnetic field corresponding to the level crossing this combination is an exact eigenstate of the Hamiltonian. For circular dots the present findings give an additional insight into the properties of the magic-angular-momenta states and into the physics behind the broken-symmetry mean-field solutions.