Protected chiral edge modes are a well-known signature of topologically ordered phases like the fractional quantum Hall states. Recently, using the framework of projected entangled pair states (PEPS) on the square lattice, we constructed a family of chiral resonating valence bond states with ${\mathbb{Z}}_2$ gauge symmetry. Here we revisit and analyze in full details the properties of the edge modes as given by their entanglement spectra on a cylinder. Surprisingly, we show that the latter can be well described by a chiral $\mathrm{SU}(2{)}_1$ conformal field theory, as for the $\nu =1/2$ (bosonic) gapped Laughlin state, although our numerical data suggest a critical bulk compatible with an emergent $\text{U}\left(1\right)$ gauge symmetry. We propose that our family of PEPS may physically describe a boundary between a chiral topological phase and a trivial phase.

• Received 27 February 2016

DOI:https://doi.org/10.1103/PhysRevB.93.174414