Séminaire Physique mathématique ICJ

Entanglement entropy in condensed matter systems

by Benoit Estienne (LPTHE, UPMC)

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne
Ideas coming from quantum information theory have provided invaluable insights and powerful tools for quantum many-body systems. One of the most basic tools in the arsenal of quantum information theory is (entanglement) entropy. A particularly striking phenomenon is the the “area law” of the entanglement entropy, which has been widely discussed in recent years in condensed matter and quantum field theories. Typically, one considers a many-particle state and a geometric partition of the space in two sub-regions. The von Neumann entropy of the reduced state of a sub-region measures the degree of entanglement between the two regions. The area law states that this entanglement entropy is proportional to the volume of the boundary of the sub-region. I will start with an introduction to quantum entanglement, entanglement entropy and their applications in condensed matter. I will then present some recent results in the context of the quantum Hall effect.