  We discuss an extension of higher order topological phases to include bosonic
systems. We present two spin models for a second-order topological phase
protected by a global $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. One model is
built from layers of an exactly solvable cluster model for a one-dimensional
$\mathbb{Z}_2\times\mathbb{Z}_2$ topological phase, while the other is built
from more conventional spin-couplings (XY or Heisenberg). These models host
gapped, but topological, edges, and protected corner modes that fall into a
projective representation of the symmetry. Using Jordan-Wigner transformations
we show that our models are both related to a bilayer of free Majorana fermions
that form a fermionic second-order topological phase. We also discuss how our
models can be extended to three-dimensions to form a third-order topological
phase.
