Benoit Estienne: Entanglement entropy in one-dimensional critical models

par Benoit Estienne

vendredi 19 sept. 2025, 09:30 → 12:00 Europe/Paris

Salle Fokko Du Cloux (Institut Camille Jordan)

Over the past twenty years, quantum entanglement has established itself as a central theme of research across a wide spectrum of physics, from high-energy theory to condensed matter and quantum information. In the context of this talk, the key point is that entanglement measures have proven to be a remarkably powerful tool for investigating the physics of one-dimensional quantum critical systems.

I will begin by introducing the relevant concepts and reviewing the replica approach to computing Rényi entropies. For one-dimensional quantum systems in particular, the entanglement entropy can be evaluated within two complementary frameworks. In the geometric perspective, the scaling limit reduces the problem to computing a partition function on a branched covering of certain Riemann surfaces—effectively a replication of space-time. In contrast, the algebraic perspective replicates the degrees of freedom themselves, leading to the formulation of a cyclic orbifold.

Following this review, I will discuss the current state of the art, highlight the main obstacles to evaluating entanglement entropies in one-dimensional quantum critical systems, and outline some recent developments in the field.