Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement

TL;DR

This paper provides exact solutions for the excitation spectra, spin configurations, and entanglement properties of three-electron anisotropic quantum dots under varying magnetic fields and anisotropies, revealing Wigner molecule formations and complex entanglement structures.

Contribution

It offers the first comprehensive exact-diagonalization analysis of three-electron quantum dots across diverse anisotropies and magnetic fields, detailing their spectra, spin arrangements, and entanglement characteristics.

Findings

Electrons tend to localize forming Wigner molecules.

Wigner molecules can form linear or complex zig-zag structures.

Entanglement quantified by von Neumann entropy varies with parameters.

Abstract

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.