Speaker
Curt von Keyserlingk
(Rudolf Peierls Centre for Theoretical Physics)
Description
Little is known about the kinds of topological phases that
exist in 3D, or how to classify them. It therefore makes
sense to investigate solvable models exhibiting topological
order. In this work we study such a class of exactly solvable
spin models, first put forward by Walker and Wang (2011).
While these are not models of interacting fermions, they
may well capture the topological behaviour of some strongly
correlated systems. In this work we give a full treatment of
a special case, which we call the 3D semion model: We
calculate its ground state degeneracies for a variety of
boundary conditions, and classify its low-lying excitations.
While point defects in the bulk are confined in meson-like
pairs, the surface excitations are more interesting: The
model has deconfined point defects pinned to the boundary
of the lattice, and these exhibit semionic statistics. The
surface physics is reminiscent of a $\nu=1/2$ bosonic
fractional quantum hall effect, and these considerations
help motivate an effective field theoretic description for the
lattice models in their topological limit based on a kind of BF
theory. Our special example of the 3D semion model
captures much of the behaviour of more general `confined
Walker-Wang models'.
