Entropy and Mutual information in low-dimensional classical and quantum critical systems
Jean-Marie Stephan, University of Virginia
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.