Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

TL;DR

This paper uses group theory to analyze symmetry breaking in two-dimensional quantum dots, linking classical configurations to quantum properties and accurately predicting energy spectra related to magic angular momenta.

Contribution

It introduces a group theoretical framework connecting classical electron arrangements to quantum symmetry breaking and restoration in quantum dots, explaining magic angular momenta phenomena.

Findings

Symmetry-broken orbitals relate to classical electron configurations.

Restoring symmetries reveals magic angular momenta in spectra.

Method accurately predicts energy levels associated with these angular momenta.

Abstract

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.