Magnetic Response of Interacting Electrons in a Fractal Network: A Mean Field Approach

The Hubbard model on a Sierpinski gasket fractal is carefully examined within a Hartree-Fock mean field approach. We examine the influence of a magnetic flux threading the gasket on its ground state energy, persistent current and the Drude weight. Both an isotropic gasket and its anisotropic counterpart have been examined. The variance in the patterns of the calculated physical quantities are discussed for two situations, viz, at half-filling and when the `band' is less than half-filled. The phase reversal of the persistent currents and the change of the Drude weight as a function of the Hubbard interaction are found to exhibit interesting patterns that have so far remained unaddressed.