Speaker
Cecile Repellin
Description
The Zk Read-Rezayi series1 is a well known sequence of
fractional quantum Hall (FQH) states with non-Abelian
topological order. The k = 1 member of this series is the
(Abelian) Laughlin state. The k = 2 member of this series is
the Moore-Read3 state supporting Majorana excitations and a
well studied candidate state for the FQH plateau of electrons
at ν = 5/2. The Zk=3 Read- Rezayi state supports Fibonacci
anyons, which can in principle be used to perform the
operations of a universal topological quantum computer. The
Zk Read-Rezayi series can be obtained using projective
constructions, by starting from the Laughlin state as a parent
state.
In the simplest version of the projective construction, the
bosonic Moore-Read state (Zk=2) is written by symmetrizing
the product of two bosonic Laughlin wave functions. On the
torus, this construction does not yield the Moore-Read state
for an odd number of particles in finite size. We show that
introducing a defect allowing the bosons to go from one layer
to the next can remedy this problem. This obstruction also
appears in the more generic case of the projective
construction of the bosonic Zk Read-Rezayi states, and is
resolved similarly. The projective construction could provide
an avenue to write higher k members of the Zk series in the
matrix product state language. In this context, our new
construction scheme should allow us to recover all topological
sectors of the SU(2)k theory starting only from the Laughlin
state. Beyond model states, the projective construction can
also be used to describe the neutral excitations above the
Read-Rezayi states. I will explore the accuracy of this
approximation in the case of the Moore-Read state neutral
mode. Finally, I will discuss the possibility that a microscopic
interlayer coupling term might physically realize the
symmetrization in a bilayer system.