Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we present a two-step approach in which a Hartree-Fock method, with explicit symmetry breaking, is followed by a projection technique for symmetry restoration. Three different Hartree-Fock implementations, with an increasing degree of symmetry breaking, are introduced and applied to the study of interacting planar dots with N = 3 and 6, electrons in the presence of a perpendicular magnetic field. In addition to the restricted and unrestricted techniques already employed for quantum dots, the general unrestricted Hartree-Fock method is described. It is characterized by a complete breaking of all spatial and spin symmetries and improved energy estimates of the ground state energy. Projection techniques suitable for all three Hartree-Fock methods are introduced, and shown to generate correlated many-body wavefunctions. © 2009 Elsevier B.V. All rights reserved.
Cavaliere F., De Giovannini U. (2010). General Hartree-Fock method and symmetry breaking in quantum dots. PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, 42(3), 606-609 [10.1016/j.physe.2009.06.081].
General Hartree-Fock method and symmetry breaking in quantum dots
De Giovannini U.
2010-01-01
Abstract
Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we present a two-step approach in which a Hartree-Fock method, with explicit symmetry breaking, is followed by a projection technique for symmetry restoration. Three different Hartree-Fock implementations, with an increasing degree of symmetry breaking, are introduced and applied to the study of interacting planar dots with N = 3 and 6, electrons in the presence of a perpendicular magnetic field. In addition to the restricted and unrestricted techniques already employed for quantum dots, the general unrestricted Hartree-Fock method is described. It is characterized by a complete breaking of all spatial and spin symmetries and improved energy estimates of the ground state energy. Projection techniques suitable for all three Hartree-Fock methods are introduced, and shown to generate correlated many-body wavefunctions. © 2009 Elsevier B.V. All rights reserved.File | Dimensione | Formato | |
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Cavaliere-General Hartree-Fock method and symmetry breaking in quantum dots-2010-Physica E- Low-dimensional Systems and Nanostructures.pdf
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