Fracton Phase in a Layered Honeycomb Lattice*

There has been much recent interest in understanding topological phases
that do not admit a traditional gauge theory description. Key
aspect of such phases is the presence of "fracton" excitations
[Vijay et al., PRB, 92, 235136] which appear at the
corners of membrane operators. This active field is being
pursued via the study of specific models. In this paper we develop
and study a model based on a layered honeycomb lattice with Ising spins that
supports a fracton phase. We demonstrate that in addition to
possessing fracton excitations (corners of membrane operators),
the phase also has excitations that occur at the ends of lines
which are confined to particular honeycomb layers. We further
investigate how this fracton phase is destroyed by a transverse field.
By means of a detailed Monte-Carlo study that uncovers the phase
diagram of this model, we discuss the transition between the
fracton phase and the trivial paramagnetic phase that sets in at
high transverse fields.