Séminaire Physique mathématique ICJ

Entanglement and conformal field theory in simple quantum Hall states

by Mr Jean Marie Stephan

Europe/Paris
Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

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

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