  We discuss symmetry breaking in two-dimensional quantum dots resulting from
strong interelectron repulsion relative to the zero-point kinetic energy
associated with the confining potential. Such symmetry breaking leads to the
emergence of crystalline arrangements of electrons in the dot. The so-called
Wigner molecules form already at field-free conditions. The appearance of
rotating Wigner molecules in circular dots under high magnetic field, and their
relation to magic angular momenta and quantum-Hall-effect fractional fillings,
is also discussed. Recent calculations for two electrons in an elliptic quantum
dot, using exact diagonalization and an approximate generalized-Heitler-London
treatment, show that the electrons can localize and form a molecular dimer for
screened interelectron repulsion. The calculated singlet-triplet splitting (J)
as a function of the magnetic field (B) agrees with cotunneling measurements;
its behavior reflects the effective dissociation of the dimer for large B.
Knowledge of the dot shape and of J(B) allows determination of two measures of
entanglement (concurrence and von Neumann entropy for indistinguishable
fermions), whose behavior correlates also with the dissociation of the dimer.
The theoretical value for the concurrence at B=0 agrees with the experimental
estimates.
