2–27 May 2016
Nordita, Stockholm
Europe/Stockholm timezone

Projective construction of the Zk Read-Rezayi fractional quantum Hall states

19 May 2016, 10:00
1h
122:026 (Nordita, Stockholm)

122:026

Nordita, Stockholm

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.

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