2 research outputs found
Hierarchy wave functions--from conformal correlators to Tao-Thouless states
Laughlin's wave functions, describing the fractional quantum Hall effect at
filling factors , can be obtained as correlation functions in
conformal field theory, and recently this construction was extended to Jain's
composite fermion wave functions at filling factors . Here we
generalize this latter construction and present ground state wave functions for
all quantum Hall hierarchy states that are obtained by successive condensation
of quasielectrons (as opposed to quasiholes) in the original hierarchy
construction. By considering these wave functions on a cylinder, we show that
they approach the exact ground states, the Tao-Thouless states, when the
cylinder becomes thin. We also present wave functions for the multi-hole
states, make the connection to Wen's general classification of abelian quantum
Hall fluids, and discuss whether the fractional statistics of the
quasiparticles can be analytically determined. Finally we discuss to what
extent our wave functions can be described in the language of composite
fermions.Comment: 9 page
Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
We analyze the non-abelian Read-Rezayi quantum Hall states on the torus,
where it is natural to employ a mapping of the many-body problem onto a
one-dimensional lattice model. On the thin torus--the Tao-Thouless (TT)
limit--the interacting many-body problem is exactly solvable. The Read-Rezayi
states at filling are known to be exact ground states of a
local repulsive -body interaction, and in the TT limit this is manifested
in that all states in the ground state manifold have exactly particles on
any consecutive sites. For the two-body correlations of these
states also imply that there is no more than one particle on adjacent
sites. The fractionally charged quasiparticles and quasiholes appear as domain
walls between the ground states, and we show that the number of distinct domain
wall patterns gives rise to the nontrivial degeneracies, required by the
non-abelian statistics of these states. In the second part of the paper we
consider the quasihole degeneracies from a conformal field theory (CFT)
perspective, and show that the counting of the domain wall patterns maps one to
one on the CFT counting via the fusion rules. Moreover we extend the CFT
analysis to topologies of higher genus.Comment: 15 page