7 research outputs found
Anyonic order parameters for discrete gauge theories on the lattice
We present a new family of gauge invariant non-local order parameters for
(non-abelian) discrete gauge theories on a Euclidean lattice, which are in
one-to-one correspondence with the excitation spectrum that follows from the
representation theory of the quantum double D(H) of the finite group H.
These combine magnetic flux-sector labeled by a conjugacy class with an
electric representation of the centralizer subgroup that commutes with the
flux. In particular cases like the trivial class for magnetic flux, or the
trivial irrep for electric charge, these order parameters reduce to the
familiar Wilson and the 't Hooft operators respectively. It is pointed out that
these novel operators are crucial for probing the phase structure of a class of
discrete lattice models we define, using Monte Carlo simulations.Comment: 14 pages, 1 figur
Charged spin textures over the Moore-Read quantum Hall state
We study the composite Charged Spin Texture (CST) over the Moore-Read quantum Hall state that arises when a collection of elementary CSTs are moved to the same location. Following an algebraic approach based on the characteristic pair correlations of the Moore- Read state, we and that the resulting CST is set by the fusion sector of the underlying non- Abelian quasiparticles. This phenomenon provides a novel way to read out the quantum register of a non-Abelian topologically ordered phas