A new class of edge theories for fermionic Abelian topological phases
Ungappable edge theories with finite dimensional Hilbert spaces
We construct a new class of edge theories for a family of fermionic fermionic topological phases with of the form where are odd integers.Our edge theories are notable for two reasons : (i) they have finite dimensional hilbertspaces (for finite sized systems) and (ii) depending on the values of some of the edge theories describe boundaries that can not be gapped by any local interaction.The simplest example of such an ungappable boundaryoccurs for which is realized by the fermionic quasi-quantum hall state.We derive our edge theories by starting with the standard chiral bosonedge theory, consisting of two counterpropagating chiral boson modes, and then introducing an array of pointlike impurity scatterers.We solve this impurity model exactly in the limit of infinite impurity scattering, and we show that the energy spectrum consists of a gapped phonon spectrum together with a ground state degeneracy that scales exponentially with the number of impurities.
Examples of edge theories for type-I and type-III topological phases. (a) A chiral boson field theory describes the edge of the (type-III) Laughlin state. (b) A spin-