Symmetry breaking and the random-phase approximation in small quantum dots

TL;DR

This paper investigates the use of the random-phase approximation to analyze symmetry breaking and correlation energies in small quantum dots, comparing results with exact calculations to evaluate its accuracy.

Contribution

It applies the random-phase approximation to small quantum dots, focusing on symmetry restoration and correlation energies, and systematically compares with exact results.

Findings

RPA effectively estimates correlation energies in quantum dots.

Symmetry restoration improves the physical accuracy of RPA results.

Validation against exact solutions confirms RPA's applicability in certain regimes.

Abstract

The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration and the role of the spurious modes within the random-phase approximation. A systematics with the Coulombic interaction strength is presented for the 2-electron dot, while for the 6- and 12-electron dots selected cases are discussed. The validity of the random-phase approximation is assessed by comparison with available exact results.