Séminaire de groupe
Entropy and mutual information in lowdimensional classical and quantum critical systems 
JeanMarie Stéphan 
University of Virginia (USA) 
vendredi 17 janvier 2014 , 10h25 
Salle de séminaire du groupe de Physique Statistique 
In studies of new and exotic phases of quantum matter, the Renyi entanglement entropy has established itself as an important resource. For example it is universal at onedimensional quantum critical points: the leading term can be used to extract the central charge $c$ of the underlying conformal field theory, and thus identify the universality class. In this talk I will show how an analogous quantity defined for classical systems, the Renyi Mutual Information (RMI), can be used to access universality classes in 2d. In particular for a rectangle cut into two rectangles, the shape dependence of the RMI can be computed exactly and is proportional to $c$. This makes it possible to extract $c$ from (transfermatrix) Monte Carlo simulations. I will also discuss how this Mutual information is related to the entanglement entropy of certain Resonating valence bond states in 2d, as well as other basisdependent entropies in 1d quantum systems. 
