Modular Groups, Visibility Diagram and Quantum Hall Effect
نویسندگان
چکیده
We consider the action of the modular group Γ(2) on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two “visibility” diagrams, the first one being associated with even denominator fractions whereas the second one is linked to odd denominator fractions. We use this model to predict, among some interesting physical quantities, the relative ratios of the width of the different transversal resistivity plateaus. A numerical simulation of the tranversal resistivity plot based on this last prediction fits well with the present experimental data. IPNO-TH-96-27 (december 1996) LPTHE Orsay 96/54 † unité de Recherche des universités Paris 11 et Paris 6 associée au CNRS * Laboratoire associé au CNRS, URA D0063
منابع مشابه
Visibility Diagrams and Experimental Stripe Structures in the Quantum Hall Effect
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 interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a st...
متن کامل1 Global quantum Hall phase diagram from visibility diagrams
We propose a construction of a global phase diagram for the quantum Hall effect. This global phase diagram is based on our previous constructions of visibility diagrams in the context of the Quantum Hall Effect. The topology of the phase diagram we obtain is in good agreement with experimental observations (when the spin effect can be neglected). This phase diagram does not show floating.
متن کاملThe global phase diagram of a modular invariant two dimensional statistical model
A generalization of the Coulomb Gas model with modular SL(2, Z)symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2, Z) acting on the two-dimensional parameter space give...
متن کاملΓ(2) Modular Symmetry, Renormalization Group Flow and the Quantum Hall Effect
We construct a family of holomorphic β-functions whose RG flow preserves the Γ(2) modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules...
متن کاملRenormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram
Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2, Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2, Z) duality between different quantum Hall fluids, we...
متن کامل