  The entanglement spectrum (ES) provides a barometer of quantum entanglement
and encodes physical information beyond that contained in the entanglement
entropy. In this paper, we explore the ES of stabilizer codes, which furnish
exactly solvable models for a plethora of gapped quantum phases of matter.
Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak
local perturbations thus allows us to develop a general framework within which
the entanglement features of gapped topological phases can be computed and
contrasted. In particular, we study models harboring fracton order, both type-I
and type-II, and compare the resulting ES with that of both conventional
topological order and of (strong) subsystem symmetry protected topological
(SSPT) states. We find that non-local surface stabilizers (NLSS), a set of
symmetries of the Hamiltonian which form on the boundary of the entanglement
cut, act as purveyors of universal non-local features appearing in the
entanglement spectrum. While in conventional topological orders and fracton
orders, the NLSS retain a form of topological invariance with respect to the
entanglement cut, subsystem symmetric systems---fracton and SSPT
phases---additionally show a non-trivial geometric dependence on the
entanglement cut, corresponding to the subsystem symmetry. This sheds further
light on the interplay between geometric and topological effects in fracton
phases of matter and demonstrates that strong SSPT phases harbour a measure of
quasi-local entanglement beyond that encountered in conventional SPT phases. We
further show that a version of the edge-entanglement correspondence,
established earlier for gapped two-dimensional topological phases, also holds
for gapped three-dimensional fracton models.
