Hierarchical Nature of the Quantum Hall Effects
arXiv:1108.1624 · doi:10.1103/PhysRevLett.108.066806
Abstract
I demonstrate that the wavefunction for a nu = n+ tilde{nu} quantum Hall state with Landau levels 0,1,...,n-1 filled and a filling fraction tilde{nu} quantum Hall state with 0 < tilde{nu} \leq 1 in the nth Landau level can be obtained hierarchically from the nu = n state by introducing quasielectrons which are then projected into the (conjugate of the) tilde{nu} state. In particular, the tilde{nu}=1 case produces the filled Landau level wavefunctions hierarchically, thus establishing the hierarchical nature of the integer quantum Hall states. It follows that the composite fermion description of fractional quantum Hall states fits within the hierarchy theory of the fractional quantum Hall effect. I also demonstrate this directly by generating the composite fermion ground-state wavefunctions via application of the hierarchy construction to fractional quantum Hall states, starting from the nu=1/m Laughlin states.
4 pages + 2 pages of supplementary material; v2: minor modifications and supplementary material added
References in corpus (4)
Cited by in corpus (10)
- Quantum Hall Physics - hierarchies and CFT techniques
- Hall Viscosity of Hierarchical Quantum Hall States
- A note contrasting two microscopic theories of the fractional quantum Hall effect
- Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
- Condensate-induced transitions and critical spin chains
- Composite Fermion states on the torus
- Adiabatic Construction of Hierarchical Quantum Hall States
- Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect
- Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect
- Particle-Hole Mirror Symmetries around the Half-Filled Shell: The Quantum Numbers and Algebraic Structure of Composite Fermions