My understanding is that the Toric code is a model with topologically non-trivial ground state. The ground state is degenerate on a Torus and is robust to local perturbations. The model has anyonic excitations and a non-zero topological entanglement entropy.
Topologically non-trivial phases seem to be distinguished from the trivial ones by a topological invariant. For example the Su-Schrieffer–Heeger (SSH) model has two phases which are distinguished by a winding number.
My question is: Is there a topological invariant for the Toric code? If yes, then what is it? If not, then is it wrong to say that topologically non-trivial phases are distinguished from trivial ones by a topological invariant? Another (perhaps unrelated) question is the following: does the Toric code have zero modes if it is put on a finite lattice with edges?
(In this question, I am referring to to the Toric code in 2D)
