Few-electron anisotropic quantum dots in low magnetic fields: exact-diagonalization results for excitations, spin configurations, and entanglement

Following earlier studies\footnote{Y. Li, C. Yannouleas, and U. Landman, arXiv:0710.4325v1 [Phys. Rev. B (2007), in press]; C. Yannouleas and U. Landman, Rep. Prog. Phys. {\bf 70}, 2067 (2007)} for $N=2-3$ electrons, exact-diagonalization calculations for $N=4-6$ electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, will be presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the magnetic field and of quantum-dot anisotropy. Analysis of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules (WMs). For strong anisotropy, the WMs acquire a linear geometry, and the wave functions with a total spin projection $S_z=(N-2)/2$ are similar to the strongly entangled $W$ states. For intermediate anisotropy, the WMs exhibit a more complex structure. The degree of entanglement can be quantified through the use of the von Neumann entropy.