General Hartree–Fock method and symmetry breaking in quantum dots

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.