Related papers: Renormalization Group Derivation of the Localizati…
Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $\nu{}$. In the…
The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $\xi$ of…
We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and…
We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with…
Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the…
We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of…
We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order…
We calculated numerically the localization length index $\nu$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $\nu = 2.593 \pm…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically…
We theoretically study the effect of long-ranged inhomogeneities on the critical properties of the integer quantum Hall transition. For this purpose we employ the real-space renormalization-group (RG) approach to the network model of the…
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the…
We investigate the scaling properties of zero temperature conductances at integer quantum Hall plateau transitions in the lowest Landau band of a two-dimensional tight-binding model. Scaling is obeyed for all energy and system sizes with…
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical…
A Wilsonian renormalization group approach is applied, in order to include effects of the higher Landau levels for quarks into a set of renormalized parameters for the lowest Landau level (LLL), plus a set of operators made of the LLL…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge…
The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical…
We use the dynamical structure factors of the quantum Hall states at $\nu=1/3$ and $\nu=1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the…