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Accueil du site > Séminaires > Séminaires 2014 > Entropy and Mutual information in low-dimensional classical and quantum systems

Mardi 7 janvier 2014-14:00

Entropy and Mutual information in low-dimensional classical and quantum systems

Jean-Marie Stéphan (Virginia Univ.)

par Gabriel LeMarié - 7 janvier 2014

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 one-dimensional 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 (transfer-matrix) 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 basis-dependent entropies in 1d quantum systems.

Post-scriptum :

contact : F. Alet