In this talk, I will outline our recent work on constructing a new class of edge theories for a family of fermionic Abelian topological phases with K-matrices of the form K= diag(k1, k2), where k1, k2 > 0 are odd integers. These edge theories are notable for two reasons: (i) they have finite-dimensional Hilbert spaces (for finite-sized systems) and (ii) depending on the values of k1, k2, some of the edge theories describe boundaries that cannot be gapped by any local interaction. The simplest example of such an ungappable boundary occurs for (k1, k2) = (1, 3), which is realized by the 2/3 FQH state. An intriguing aspect of these edge theories is that they do not seem to have an obvious description as a tensor product Hilbert space.
References: SG, Michael Levin arXiv:2109.11539 (talk based on)
Phys. Rev. B 93, 075118 (2016) (Method paper).