Interaction-Induced Symmetry Breaking in Circular Quantum Dots

TL;DR

This paper clarifies the nature of symmetry breaking in circular quantum dots, distinguishing between interference effects and true interaction-driven Wigner molecules, and confirms their existence using advanced neural-network Monte Carlo simulations.

Contribution

It provides a precise definition of interaction-induced Wigner molecules and demonstrates their existence with high-accuracy neural-network variational Monte Carlo methods.

Findings

Interference effects cause anisotropic patterns in non-interacting limits.

True Wigner molecules require a symmetry-breaking perturbation in strongly interacting dots.

Neural-network variational Monte Carlo outperforms traditional methods in accuracy.

Abstract

This paper investigates interaction-induced symmetry breaking in circular quantum dots. We explain that the anisotropic static Wigner molecule ground states frequently observed in simulations are created by interference effects that occur even in the non-interacting limit. They have nothing in common with the interaction-driven crystallization of the uniform electron gas described by Wigner. This leads us to define the term Wigner molecule more carefully, via a finite analog of the spontaneous symmetry breaking that arises in the homogeneous electron gas when the interactions are strong. According to this definition, the charge density patterns characteristic of true interaction-induced Wigner molecules can only be seen if a small symmetry-breaking perturbation is applied to a strongly interacting quantum dot. A simple argument based on separation of variables into center-of-mas and internal coordinates shows that the strength of the perturbation required to produce a finite effect on the density tends to zero in the limit as the strength of the interaction tends to infinity. We confirm computationally that interaction-induced Wigner molecules satisfying these two criteria exist. The neural-network variational Monte Carlo method used in our simulations proves more accurate than the coupled cluster and diffusion Monte Carlo methods employed in previous benchmark calculations of quantum dots.