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

Régis Mélin (1) , Benoît Douçot (2) , F. Iglói

1 CRTBT - Centre de Recherches sur les Très Basses Températures
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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 $\phi_0=h/e$ periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant $\phi_0/2$ 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.

Domaines: Autre [cond-mat.other]

Régis Mélin, Benoît Douçot, F. Iglói. Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2005, 72, pp.024205. ⟨hal-00102589⟩