On the degeneracy of $SU(3{)}_k$ topological phases

Abstract

The ground state degeneracy of an $SU(N{)}_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any $N>2$. Here we present the problem in an explicit combinatorial way and analyze the case N=3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.

5 pages