Crossover from Fermi Liquid to Wigner Molecule Behavior in Quantum Dots

Abstract

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover governed only by the density parameter ${r}_{s}$. For ${r}_{s}>{r}_{c}$, the data are consistent with a Wigner molecule description, while, for ${r}_{s}<{r}_{c}$, Fermi liquid behavior is recovered. The crossover value ${r}_{c}\ensuremath{\approx}4$ is surprisingly small.