Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For convenience, let's consider a 2D lattice system with $N$ lattice sites, and we may consider the finite system with open boundary condition(OBC) or periodic boundary condition(PBC). Now there are two kinds of topological degeneracy:

(1)The topological degeneracy is **approximate** for finite $N$ no matter with OBC or PBC, and it becomes **exact degenerate** only under the thermodynamic limit($N\rightarrow \infty $). **Example:** FQHE.

(2)The topological degeneracy(>1) is **exact** for **any finite $N$** with **PBC(on a torus)**, and it's **nondegenerate** for **any finite** $N$ with **OBC**. **Example:** Kitaev's toric code model.

Is there any other kind(in the above sense) of topological degeneracy?

This post imported from StackExchange Physics at 2014-03-09 08:40 (UCT), posted by SE-user K-boy