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In studies of quantum phases of matter, the entanglement entropy has established itself as an important practical 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. I will show how an analogous information theoretic 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. 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. In all cases, the information theoretic approach provides an efficient way of identifying the various competing orders in a given classical or quantum system.

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Jean-Marie Stephan
Seminar Room of the Institute for Theoretical Physics
Contact: Johannes Helmes