  The classification of electron systems according to their topology has been
at the forefront of condensed matter research in recent years. It has been
found that systems of the same symmetry, previously thought of as equivalent,
may in fact be distinguished by their topological properties. Moreover, the
non-trivial topology found in some insulators and superconductors has profound
physical implications that can be observed experimentally and can potentially
be used for applications. However, characterizing a system's topology is not
always a simple task, even for a theoretical model. When translation and other
symmetries are present in a quadratic model the topological invariants are
readily defined and easily calculated in a variety of symmetry classes.
However, once interactions or disorder come into play the task becomes
difficult, and in many cases prohibitively so. The goal of this paper is to
suggest alternatives to the topological invariants which are based on the
entanglement spectrum and entanglement entropy. Using quadratic models of
superconductors we demonstrate that these entanglement properties are sensitive
to changes in topology. We choose quadratic models since the topological phase
diagram can be mapped using the topological invariants and then compared to the
entanglement entropy/spectrum features. This work sets the stage for learning
about topology in interacting and disordered systems through their entanglement
properties.
