A new class of edge theories for fermionic Abelian topological phases

Ungappable edge theories with finite dimensional Hilbert spaces

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-

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.

We construct edge theories for two dimensional topological phases that are fundamentally different from the well known chiral boson field theory that describes the edge of the (type-1) fractional quantum hall state.

In particular we wish to find edge theories that have a dimensional hilbert space for a finite size system.

Such edge theories are desirable because they provide a simple and well-regulated setting to study edge physics.