Speaker
Matthias Troyer (ETH)
Description
In quasi-two-dimensional systems non-abelian anyons can
appear as quasiparticle excitations next to fermions and
bosons. They have been proposed to appear, among other
potential realizations, in certain fractional quantum Hall
states. These non-Abelian anyons have non-trivial braiding
statistics and can be used to realize a universal
topological quantum computer. In this talk I will focus on
interactions between such anyons and the plethora of
possible ground states in systems of interacting anyons. For
one-dimensional arrangements of anyons there are close
connections to the minimal models of conformal field theory
which can be viewed as generalized Heisenberg models. In two
dimensions we find that unlike for localized fermions, where
a gapless symmetry-broken Neel state is formed, the ground
state of an array of localized anyons is another chiral
anyonic quantum Hall liquid
