Phase Transitions of Bipartite Entanglement

I will introduce a random matrix model for the statistical properties ofthe partial purity of a pure state in a bipartite quantum system at afinite fictitious temperature. This enables one to write the generatingfunction for the cumulants, for both balanced and unbalancedbipartitions. It also unveils an unexpected feature of the system,namely the existence of two phase transitions, characterized bydifferent spectra of the partial density matrices. One of the criticalphases is described by the statistical mechanics of 2-D gravity, theother is a second-order phase transition.