Title: A simple anisotropic three-dimensional quantum spin liquid with fracton topological order,
Abstract: We present a three-dimensional cubic lattice spin model, anisotropic in the
$\hat{z}$ direction, that exhibits fracton topological order. The latter is a
novel type of topological order characterized by the presence of immobile
pointlike excitations, named fractons, residing at the corners of an operator
with two-dimensional support. As other recent fracton models, ours exhibits a
subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$
three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional
non-topological degeneracy equal to $2^{L_xL_y-2}$. The fractons can be
combined into composite excitations that move either in a straight line along
the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$.
While our model draws inspiration from the toric code, we demonstrate that it
cannot be adiabatically connected to a layered toric code construction.
Additionally, we investigate the effects of imposing open boundary conditions
on our system. We find zero energy modes on the surfaces perpendicular to
either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces
normal to $\hat{z}$. This result can be explained using the properties of the
two kinds of composite two-fracton mobile excitations.