Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

Energy spectra, electron densities, pair correlation functions and heat capacity of a quantum-dot lithium in zero external magnetic field (a system of three interacting two-dimensional electrons in a parabolic confinement potential) are studied using the exact diagonalization approach. A particular attention is given to a Fermi-liquid -- Wigner-solid transition in the ground state of the dot, induced by the intra-dot Coulomb interaction.

The interplay of confinement and Coulomb interactions in quantum dots can lead to strongly correlated phases differing qualitatively from the Fermi liquid behavior. We explore how the presence of magnetic impurities in quantum dots can provide additional opportunities to study correlation effects and the resulting ordering in carrier and impurity spin. By employing exact diagonalization we reveal that seemingly simple two-carrier quantum dots lead to a rich phase diagram. We ...

We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter $\alpha$ from the Hartree-Fock approximation and, alternatively, by employing the M\"uller exchange f...

We study the crossover between liquid and solid electron phases in a two-dimensional harmonic trap as the density is progressively diluted. We infer the formation of geometrically ordered phases from charge distributions and pair correlation functions obtained via a large scale configuration interaction calculation.

Using the path integral Monte Carlo technique we show that semiconductor quantum rings with up to six electrons exhibit a temperature, ring diameter, and particle number dependent transition between spin ordered and disordered Wigner crystals. Due to the small number of particles the transition extends over a broad temperature range and is clearly identifiable from the electron pair correlation functions.

We report calculations for electronic ground states of parabolically confined quantum dots for up to 30 electrons based on the quantum Monte Carlo method. Effects of the electron-electron interaction and the response to a magnetic field are exposed. The wavefunctions and the ground state energies are compared with purely classical calculations performed with a comprehensive Molecular Dynamics code. For the chosen well parameters a close correspondence in the overall shape of ...

ew-electron systems confined in quasi one-dimensional quantum dots are studied by the configuration interaction approach. We consider the parity symmetry of states forming Wigner molecules in large quantum dots and find that for the spin-polarized Wigner molecules it strictly depends on the number of electrons. We investigate the spatial spin-ordering in the inner coordinates of the quantum system and conclude that for small dots it has a short-range character and results mai...

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, th...

The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/r potential. We review a series of exact numerical results obtained in the presence of weak site disorder for fully polarized electrons (spinless fermions) and when the spin degrees of freedom are included. A novel intermediate regime between the Fermi system of weakly interacting localized pa...

We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we st...