In quantum many-body physics, topological degeneracy is a phenomenon in which the ground state of a gapped many-body Hamiltonian becomes degenerate in the limit of large system size such that the degeneracy cannot be lifted by any local perturbations.
In particular, the topological degeneracy on torus is equal to the number of quasiparticles types.
[11] In certain generalized cases, one can also design the systems with topological interfaces enriched or extended by global or gauge symmetries.
[12] The topological degeneracy also appear in non-interacting fermion systems (such as p+ip superconductors[13]) with trapped defects (such as vortices).
In non-interacting fermion systems, there is only one type of topological degeneracy where number of the degenerate states is given by