Related papers: Renormalization Group Derivation of the Localizati…
We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green's…
Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling…
We study the localization properties in the transition from a two-dimensional electron gas at zero magnetic field into an integer quantum Hall (QH) liquid. By carrying out a direct calculation of the localization length for a finite size…
While the simplest quantum Hall plateaus, such as the $\nu = 1/3$ state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher Landau…
The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to…
We show that the Landau quantum systems (or integer quantum Hall effect systems) in a plane, sphere or a hyperboloid, can be explained in a complete meaningful way from group-theoretical considerations concerning the symmetry group of the…
Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short…
A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of…
We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in…
Double-layer quantum Hall systems at Landau level filling factor $\nu=1$ have a broken symmetry ground state with spontaneous interlayer phase coherence and a gap between symmetric and antisymmetric subbands in the absence of interlayer…
Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
We propose a geometric mechanism for fractional quantum Hall states based on impurity-induced correlations within a Landau level. A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through…
We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be…
The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…
We investigate the quantum Hall effect in a single Landau level in the presence of a square superlattice of $\delta$-function potentials. The interplay between the superlattice spacing $a_s$ and the magnetic length $\ell_B$ in clean system…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free…
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…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…