A Variational Approach to Topological Degeneracy in Superconductors
In the literature, the standard method of enumerating the groundstates of superconductors is by constructing an appropriate algebra of unitary operators on the groundstate subspace. Here, we explore an alternative route to topological degeneracy in superconductors, by examining Taubes's Vortices and Monopoles, and extracting topological degeneracy as a topological factor arising from restricting to gauge-transformations of electrons. This variational argument is conjectured by Oshikawa to be equivalent mathematically to the traditional braiding argument. We make significant headway in proving this equivalence in sections III and IV.