Related papers: Modular Groups, Visibility Diagram and Quantum Hal…
We analyze the action of the inhomogeneous modular group $\Gamma (2)$ on the three cusps of its principal fundamental domain in the Poincare half plane. From this, we obtain an exhaustive classification of the fractional quantum Hall…
We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical…
An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…
We study the possible phase transitions between (2+1)-dimensional abelian Chern-Simons theories. We show that they may be described by non-unitary rational conformal field theories with c_eff = 1. As an example we choose the fractional…
An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall…
It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed…
At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We construct a family of holomorphic $\beta$-functions whose RG flow preserves the $\Gamma(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall…
The parallel roles of modular symmetry in ${\cal N}=2$ supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -- magnetic…
The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We…
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
Integer and fractional quantum Hall effects were studied with different physics models and explained by different physical mechanisms. In this paper, the common physical mechanism for integer and fractional quantum Hall effects is studied,…