Renormalization-group potential for quantum Hall effects

Renormalization group for network models of Quantum Hall transitions

We analyze in detail the renormalization group flows which follow from the recently proposed all orders β functions for the Chalker-Coddington network model. The flows in the physical regime reach a true singularity after a finite scale transformation. Other flows are regular and we identify the asymptotic directions. One direction is in the same universality class as the disordered XY model. T...

The Renormalization Group and Quantum Hall Edge States

The role of edge states in phenomena like the quantum Hall eeect is well known. In this paper we show how the choice of boundary conditions for a one-particle Schrr odinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic eld. In each case, edge states arise from a non-...

Percolation, Renormalization and the Quantum-Hall Transition

In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At the central stage shall be the real-space renormalization group treatment of the percolation problem. As a rather novel application of this approach to percola...

Percolation, Renormalization and the Quantum-Hall Transition

Quantum renormalization of the spin Hall effect.

By quantum Monte Carlo simulation of a realistic multiorbital Anderson impurity model, we study the spin-orbit interaction (SOI) of an Fe impurity in Au host metal. We show, for the first time, that the SOI is strongly renormalized by the quantum spin fluctuation. Based on this mechanism, we can explain why the gigantic spin Hall effect in Au with Fe impurities was observed in recent experiment...