  Energy spectra, spin configurations, and entanglement characteristics of a
system of four electrons in lateral double quantum dots are investigated using
exact diagonalization (EXD), as a function of interdot separation, applied
magnetic field, and strength of interelectron repulsion. A distinctly different
quantum behavior is found compared to that of circular single quantum dots. As
a function of the magnetic field, the energy spectra exhibit a low-energy band
consisting of a group of six states, with the number six being a consequence of
the conservation of the total spin of the four electrons and the ensuing spin
degeneracies. These six states appear to cross at a single value of the
magnetic field, with the crossing point becoming sharper for larger interdot
distances. As the strength of the Coulomb repulsion increases, the six states
tend to become degenerate and a well defined energy gap separates them from the
higher-in-energy excited states.
  The appearance of the low-energy band is a consequence of the formation of a
Wigner supermolecule, with the four electrons (two in each dot) being localized
at the vertices of a rectangular parallelogram. Using the spin-resolved
pair-correlation functions, one can map the EXD many-body wave functions onto
the spin functions associated with the four localized electrons. Analogies with
nanomagnets, such as finite Heisenberg clusters, are discussed. The ability to
determine associated spin functions enables investigations concerning
entanglement properties of the system of four electrons. In particular, the
formation of Wigner supermolecules generates EXD solutions belonging to the
class of strongly entangled states referred to as N-qubit Dicke states in the
quantum-information literature.
