Theory of topological edges and domain walls.

We investigate domain walls between topologically ordered phases in two spatial dimensions. We present a method which allows for the determination of the superselection sectors of excitations of such walls and which leads to a unified description of the kinematics of a wall and the two phases to either side of it. This incorporates a description of scattering processes at domain walls which can be applied to questions of transport through walls. In addition to the general formalism, we give representative examples including domain walls between the Abelian and non-Abelian topological phases of Kitaev's honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions.

Broken quantum symmetry and confinement phases in planar physics.

Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasitriangular Hopf algebras). In this Letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it provides an effective tool for analyzing a wide variety of phases exhibiting many distinct confinement phenomena.