Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

We present detailed results of Unrestricted Hartree-Fock (UHF) calculations for up to eight electrons in a parabolic quantum dot. The UHF energies are shown to provide rather accurate estimates of the ground-state energy in the entire range of parameters from high densities with shell model characteristics to low densities with Wigner molecule features. To elucidate the significance of breaking the rotational symmetry, we compare Restricted Hartree-Fock (RHF) and UHF. While U...

The one-- and two-- particle densities of up to four interacting electrons with spin, confined within a quasi one--dimensional ``quantum dot'' are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute localized Wigner--type electron arrangement is investigated. The influence of the long range part of the Coulomb interaction is studied. When the interaction is exponentially cut off the ``crystallized'' Wigner molecule ...

Exact-diagonalization studies of few-electron quantum dots and disks are performed, with the aim to investigate a Wigner cluster -- Fermi liquid crossover in zero magnetic field at varying strength of Coulomb interaction. A clear indication of a transition of a liquid-solid type in the ground state is found in a more adequate quantum-disk model.

We investigate the properties of many-electron systems in two-dimensional polygonal (triangle, square, pentagon, hexagon) potential wells by using the density functional theory. The development of the ground state electronic structure as a function of the dot size is of particular interest. First we show that in the case of two electrons, the Wigner molecule formation agrees with the previous exact diagonalization studies. Then we present in detail how the spin symmetry break...

We explore correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but ...

The few-body problem (with $N \leq 6$ fermionic charge carriers) in isolated moir\'{e} quantum dots (MQDs) in transition metal dichalcogenide (TMD) bilayer materials with integer fillings, $\nu \geq 2$, is investigated by employing large-scale full configuration interaction (FCI, also termed exact-diagonalization) computations, and by performing a comparative analysis of the ensuing first-order (charge densities, CDs) and second-order (conditional probability distributions, C...

Accurate thermodynamic simulations of correlated fermions using path integral Monte Carlo (PIMC) methods are of paramount importance for many applications such as the description of ultracold atoms, electrons in quantum dots, and warm-dense matter. The main obstacle is the fermion sign problem (FSP), which leads to an exponential increase in computation time both with increasing the system-size and with decreasing temperature. Very recently, Hirshberg et al. [J. Chem. Phys. 1...

The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These states are of crystalline character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66, 115315 (2002)]...

The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the ground state wave function at large imaginary time. In this work, we show that optimized fourth-order Path Integral Monte Carlo methods, which use no more than 5 free-fermion propagators, can yield accurate quantum dot energies for up to 20 pola...

The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated...