Progress on the entanglement spectra of fractional quantum Hall states

A celebrated theoretical approach to the Fractional Quantum Hall Effect consists in cooking up trial wavefunctions for various filling fractions. Some specific trial states (the ones given by conformal blocks) have particularly nice properties. Physically, they describe exotic phases of matter, for instance with non-abelian excitations. On the technical side, they bear some striking resemblance with Tensor Product States. The purpose of this talk is to explain how the edge excitations and the entanglement spectrum of these states both arise naturally from their underlying CFT structure.