1,750 research outputs found
Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
We demonstrate numerically that non-Abelian quasihole excitations of the fractional quantum Hall state have some of the key properties necessary
to support quantum computation. We find that as the quasihole spacing is
increased, the unitary transformation which describes winding two quasiholes
around each other converges exponentially to its asymptotic limit and that the
two orthogonal wavefunctions describing a system with four quasiholes become
exponentially degenerate. We calculate the length scales for these two decays
to be and
respectively. Additionally we determine which fusion channel is lower in energy
when two quasiholes are brought close together.Comment: 4 pages, 3 figure
Ashkin-Teller universality in a quantum double model of Ising anyons
We study a quantum double model whose degrees of freedom are Ising anyons.
The terms of the Hamiltonian of this system give rise to a competition between
single and double topologies. By studying the energy spectra of the Hamiltonian
at different values of the coupling constants, we find extended gapless regions
which include a large number of critical points described by conformal field
theories with central charge c=1. These theories are part of the Z_2 orbifold
of the bosonic theory compactified on a circle. We observe that the Hilbert
space of our anyonic model can be associated with extended Dynkin diagrams of
affine Lie algebras which yields exact solutions at some critical points. In
certain special regimes, our model corresponds to the Hamiltonian limit of the
Ashkin-Teller model, and hence integrability over a wide range of coupling
parameters is established.Comment: 11 pages, minor revision
Non-Abelian anyons: when Ising meets Fibonacci
We consider an interface between two non-Abelian quantum Hall states: the
Moore-Read state, supporting anyons of Ising type, and the k=2 NASS
(non-Abelian spin-singlet) state, supporting anyons of Fibonacci type. It is
shown that the interface supports neutral excitations described by a 1+1
dimensional conformal field theory with central charge c=7/10. We discuss
effects of the mismatch of the quantum statistical properties of the
quasi-holes between the two sides, as reflected by the interface theory.Comment: As published in PR
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