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Title:
Exploring the non-Abelian quantum Hall landscape with duality
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Abstract:
It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases accessible to physically motivated theories of Abelian composite particles. We show that progress can be made using the recently proposed family of non-Abelian boson-fermion dualities in two spatial dimensions. In the quantum Hall context, these dualities connect the dynamics of the ordinary, Abelian composite particles to dual, non-Abelian degrees of freedom, for which non-Abelian topological orders may be more transparently accessible, for example through pairing or filling of Landau levels. In this talk, we will focus on the particular example of the Fibonacci FQH state of bosons at filling ν = 2. Despite its salience as the simplest platform for a universal topological quantum computer, a dynamical picture for how this state might arise in a quantum Hall system has been lacking. By using duality with a theory of bosonic "composite vortices" coupled to an emergent U(2) gauge field, we present a construction of this state starting from a trilayer system with two trivial layers and one with the Halperin (2,2,1) topological order. The Fibonacci state is obtained when the composite vortices are clustered between the layers. We further leverage this approach to motivate the first proposal for an ideal wave function for the Fibonacci state.
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