Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus
نویسنده
چکیده
One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.
منابع مشابه
Modular Invariance on the Torus and Fractional Quantum Hall Effect
The implementation of modular invariance on the torus at the quantum level is discussed in a group-theoretical framework. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is ev...
متن کاملHierarchical wave function, Fock cyclic condition, and spin-statistics relation in the spin-singlet fractional quantum Hall effect.
We construct the hierarchical wave function of the spin-singlet fractional quantum Hall effect, which turns out to satisfy Fock cyclic condition. The spin-statistics relation of the quasi-particles in the spin-singlet fractional quantum Hall effect is also discussed. Then we use particle-hole conjugation to check the wave function. PACS numbers: 73.20.Dx, 05.30.-d ⋆ email: [email protected]
متن کاملHierarchical Wave Functions of Fractional Quantum Hall Effect on the Torus
One kind of the hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions closely relate to the wave functions of generalized Abelian Chern-Simons theory. ⋆ emai: [email protected] The past ten years have seen a great deal of interest in Fractional Quantum Hall Effect not only in the group of the condense matter physicists, but...
متن کاملHierarchical Wave Functions Revisited
The trial wave function of the fractional quantum Hall effect (FQHE) on a disk at filling ν = 1/m with m an old integer is given by the famous Laughlin wave function [1]. Laughlin wave function had been constructed on a spheric or a toric surface later in refs. [2, 3]. When ν 6= 1/m, there are several proposals for constructing the trial wave function, notably Halperin’s hierarchical wave funct...
متن کاملConformal field theory approach to bulk wave functions in the fractional quantum Hall effect
We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of nonunitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain. Fractional statistics is described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bu...
متن کامل