We perform unrestricted Hartree-Fock (HF) calculations for electrons in a parabolic quantum dot at zero magnetic field. The crossover from Fermi liquid to Wigner molecule behavior is studied for up to eight electrons and various spin components $S_z$. We compare the results with numerically exact path-integral Monte Carlo simulations and earlier HF studies. Even in the strongly correlated regime the symmetry breaking HF solutions provide accurate estimates for the energies and describe the one-particle densities qualitatively. However, the HF approximation favors the formation of a Wigner molecule and produces azimuthal modulations of the density for even numbers of electrons in one spatial shell.Comment: 5 pages, figures include

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 UHF symmetry breaking admits lower ground-state energies, misconceptions in the interpretation of UHF densities are pointed out. An analysis of the orbital energies shows that for very strong interaction the UHF Hamiltonian is equivalent to a tight-binding Hamiltonian. This explains why the UHF energies become nearly spin independent in this regime while the RHF energies do not. The UHF densities display an even-odd effect which is related to the angular momentum of the Wigner molecule. In a weak transversal magnetic field this even-odd effect disappears. PACS numbers: 73.21.La,31.15.Ne,71.10.Hf II. HAMILTONIAN AND HARTREE-FOCK APPROXIMATIONIn this work we follow the notation and method presented in our earlier article 6 for zero magnetic field. The Hamiltonian of an isotropic parabolic quantum dot with magnetic field reads (see e.g. Refs. 1

Abstract. -Numerically exact path-integral Monte Carlo data are presented for N ≤ 10 strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers N = 4, 6, 9, corresponding to peaks in the addition energy ∆(N ), is destroyed, with a new peak at N = 8, (2) spin gaps decrease, (3) for N = 8, sub-Hund's rule spin S = 0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.During the past few years, the electronic properties of 2D quantum dots have been the subject of intense theoretical studies [1,2]. A particularly interesting aspect of such artificial atoms is the wide experimental tunability of the electron number N and the Brueckner interaction strength parameter r s in high-quality semiconductor dots [3,4,6]. In particular, it has been established both theoretically [1,7] and experimentally [8,9] that a "Wigner molecule" of crystallized electrons forms already at surprisingly high densities corresponding to r s > ∼ 2 [10]. In this paper, we present numerically exact path-integral Monte Carlo (PIMC) [11] simulation results for N ≤ 10 electrons in the most challenging incipient Wigner molecule regime, choosing r s ≈ 4. Due to the breakdown of effective single-particle descriptions, this parameter regime is notoriously difficult to treat within approximation schemes such as Hartree-Fock theory [1], density functional theory [1,12,13], semiclassical [14] or classical [15] approaches. Especially concerning disordered dots, in the absence of benchmark calculations, their accuracy has so far been largely unclear.The incipient Wigner molecule regime also exhibits unexpected and interesting physics, in particular rather dramatic effects when including just one impurity in order to break rotational symmetry. Below we shall demonstrate this in three different ways. First, despite the presence of strong interactions, the clean system still exhibits shell structure, with exceptional stability of the dot for "magic numbers" N = 4, 6, and 9. The stability is reflected in peaks in the corresponding addition energy, ∆(N ) = E(N + 1) − 2E(N ) + E(N − 1),c EDP Sciences

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