Related papers: Anderson Localization and Quantum Hall Effect: Num…
We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are…
In the composite fermion model of the fractional quantum Hall effect, composite fermions experience, in addition to the usual potential disorder, also a magnetic flux disorder. Motivated by this, we investigate the localization properties…
Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity $\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the…
We review the implications of the scaling data for the emergent symmetry of the quantum Hall system. The location of the fixed points in the conductivity plane is consistent with the global, non-Abelian discrete symmetry $\Gamma _{0}(2)$,…
The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
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…
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…
Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution…
We obtain a ``mean field'' scaling flow of the longitudinal and the Hall conductivities in the fractional quantum Hall regime. Using the composite fermion picture and assuming that the composite fermions follow the Khmelnitskii-Pruisken…
Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
We present a renormalization group analysis of the problem of Anderson localization on a Random Regular Graph (RRG) which generalizes the renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional…
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…
In order to study an interplay of disorder, correlation, and spin imbalance on antiferromagnetism, we systematically explore the ground state of one-dimensional spin-imbalanced Anderson-Hubbard model by using the density-matrix…
The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
The two-parameter renormalization group flow diagramme is used for obtaining the magnetic field dependence of localisation length Lc(B) for charged particles in 2D random potential at low disorder and weak magnetic fields B. The result…