Séminaire Physique mathématique ICJ

Entanglement and conformal field theory in simple quantum Hall states

by Mr Jean Marie Stephan

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne

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.

Organized by

Nguyen-Viet Dang