摘要：Doubled topological phases introduced by Kitaev, Levin, and Wen supported
on two-dimensional lattices are Hamiltonian versions of three-dimensional
topological quantum field theories described by the Turaev-Viro state
sum models. We introduce the latter with an emphasis on obtaining them
from theories in the continuum. Equivalence of the previous models in the
ground state is shown in case of the honeycomb lattice and the gauge group
being a finite group by means of the well-known duality transformation between
the group algebra and the spin network basis of lattice gauge theory.
An analysis of the ribbon operators describing excitations in both types of
models and the three-dimensional geometrical interpretation are given.
