1108.1624 (Parsa Bonderson)

Hierarchical Nature of the Quantum Hall Effects    [PDF]

Parsa Bonderson

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.

View original: http://arxiv.org/abs/1108.1624