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

TL;DR

This paper applies a numerical strong disorder renormalization group method to fractal lattices, revealing new fixed points in Heisenberg models and analyzing magnetoresistive effects in disordered tight-binding models.

Contribution

It introduces a numerical approach to study low-energy fixed points of disordered models on fractal lattices, discovering new fixed points and analyzing magnetoresistive phenomena.

Findings

New types of infinite and strong disorder fixed points in Heisenberg models.

Dominant /h periodicity in lattices with even-site plaquettes.

/2 periodicity and weak localization-like magnetoconductance in certain 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 $\phi_0=h/e$ 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.