Jean-Marie Stephan

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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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Seminar Room of the Institute for Theoretical Physics
Contact: Johannes Helmes