In this talk, I will present recent results in the entanglement
entropy of gapped quantum phases of matter. In particular, I will
focus on the following two results:
-
The topological entanglement entropy for some of the known topological
states in three and higher dimensions has an interesting dependence on
the Betti numbers of the boundary manifold defined by the entanglement
cut.
-
In contrast to the familiar result in two dimensions, a size independent
constant contribution to the entanglement entropy can appear for
non-topological phases in any odd spatial dimension.
Work done with Ari Turner and Ashvin Vishwanath,
reference:
http://arxiv.org/abs/1108.4038