Entanglement entropy (EE) is a measure of the amount of entanglement in a many body quantum wavefunction, given a bipartition of the Hilbert space. While the phenomenon of entanglement is arguably a mysterious aspect of quantum mechanics, EE has also been used as a practical tool to investigate and classify phases of matters at low temperatures.
For one dimensional quantum systems described by a conformal field theory (CFT), the EE is widely believed to be proportional to the central charge of the underlying CFT. In this talk, I will investigate simple two-dimensional wavefunctions that occur in the study of the quantum Hall effect. Some of these states are related to ensembles of complex random matrices, and classical two-dimensional Coulomb gases.
For such wavefunctions, only the one-dimensional boundary is a CFT in some appropriate scaling limit. I will explain how the "boundary modes" are expected to affect entanglement depending on the bipartition, and discuss two examples where the result can be proved.