Interaction-induced symmetry breaking in circular quantum dots

Abstract

This paper investigates interaction-induced symmetry breaking in circular quantum dots. We start by explaining what is known about symmetry breaking in quantum dots, pointing out 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-mass 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 this definition 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 at small to intermediate interaction strengths. For high interaction strengths, our neural-network variational Monte Carlo energies agree very well with existing fixed-node diffusion Monte Carlo benchmarks, proving ∼0.01% better for small values of the total spin projection Sz but ∼0.01% worse for fully spin-polarized systems.