Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models

Abstract

We use a numerical implementation of the strong disorder renormalization group (RG) method to study the low-energy fixed points of random Heisenberg and tight-binding models on different types of fractal lattices. For the Heisenberg model new types of infinite disorder and strong disorder fixed points are found. For the tight-binding model we add an orbital magnetic field and use both diagonal and off-diagonal disorder. For this model besides the gap spectra we study also the fraction of frozen sites, the correlation function, the persistent current and the two-terminal current. The lattices with an even number of sites around each elementary plaquette show a dominant ${\varphi }_0=h/e$ periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant ${\varphi }_0/2$ periodicity at vanishing diagonal disorder, with a positive weak localization-like magnetoconductance at infinite disorder fixed points. The magnetoconductance with both diagonal and off-diagonal disorder depends on the symmetry of the distribution of on-site energies.

19 pages, 20 figures

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• Strong Disorder RG principles within a fixed cell-size real space renormalization : application to the Random Transverse Field Ising model on various fractal lattices
• Strongly disordered Hubbard model in one dimension: spin and orbital infinite randomness and Griffiths phases
• Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy