Spin and rotational symmetries in unrestricted Hartree Fock states of quantum dots

Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted Hartree Fock approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons.Comment: 16 Pages, 2 figures, accepted for publication on New Journal of Physic

Spin and rotational symmetries in unrestricted Hartree-Fock states of quantum dots

Ground state energies are obtained using the unrestricted Hartree-Fock (HF) method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund's first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted HF approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

New Journal of Physics Spin and rotational symmetries in unrestricted Hartree-Fock states of quantum dots

Abstract. Ground state energies are obtained using the unrestricted HartreeFock (HF) method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund's first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted HF approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons

Spin projected unrestricted Hartree-Fock ground states for harmonic quantum dots

We report results for the ground state energies and wave functions obtained by projecting spatially unrestricted Hartree Fock states to eigenstates of the total spin and the angular momentum for harmonic quantum dots with $N\leq 12$ interacting electrons including a magnetic field states with the correct spatial and spin symmetries have lower energies than those obtained by the unrestricted method. The chemical potential as a function of a perpendicular magnetic field is obtained. Signature of an intrinsic spin blockade effect is found.Comment: 12 pages, 5 tables, 10 figures, submitted to Phys. Rev.

Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semicoductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include: (I) Chemical bonding, dissociation, and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot. (II) Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. (III) At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4. 95 pages with 37 color figures. To download a copy with high-quality figures, go to publication #82 in http://www.prism.gatech.edu/~ph274cy

Magnetic field dependence of quantum dot ground states

We study the ground states of a planar quantum dot with N = 5, 6, 7 electrons, in the presence of a perpendicular magnetic field. Using a spatially unrestricted Hartree Fock technique followed by spin and angular momentum symmetry restoration, chemical potentials are calculated and transitions between different ground states are identified. A spin blockade in the 6 → 7 transition is found. The structure of the quantum dot wave functions is illustrated by their electron densities

Spin and rotational symmetries in unrestricted Hartree-Fock states of quantum dots New Journal of Physics Spin and rotational symmetries in unrestricted Hartree-Fock states of quantum dots

Abstract. Ground state energies are obtained using the unrestricted HartreeFock (HF) method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund's first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted HF approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons