Séminaire de Physique ThéoriqueThe entanglement entropy in integrable QFT
Benjamin Doyon (King's College London)
Thursday 20 October 2011 14:00 - Tours - Salle 1180 (Bât E2)
I will review the works I have done with my collaborators J. Cardy and O. A. Castro Alvaredo concerning the entanglement entropy (EE) in (integrable or not) quantum field theory (QFT). The EE is a measure of the quantity of entanglement between complementary sectors of observables in quantum systems. It is a good measure because it cannot increase under local unitary transformations or classical communications; but also, it turns out that it contains a lot of "universal" information about the quantum state. We have studied it in extended quantum systems near to critical points, where we looked at entanglement between various spatial regions in the ground state. Such systems display universality and are described by QFT models, and we have used the powerful mathematical structure of integrable QFT, and at times just general QFT principles, in order to extract interesting results. We showed for instance how to evaluate the EE using branch-point twist fields and partition functions on branched Riemann surfaces, and deduced how it is connected to the particle spectrum of the QFT or to the boundary entropy. I will recall the basics of entanglement entropy, and review these results and ideas.