I propose during this seminar to present some recent ideas to characterize phases using entanglement following quantum information development.

I will particularly focus on the notion of mutual information (that can be derived from the the entanglement entropy) as a mean to detect topological matter (mostly 2D) as introduced with the topological entanglement entropy (see PhysRevLett.96.110405 or PhysRevLett.96.110404).

This seminar aims at a discussion on the subject and hence will take the time to provide the necessary background for the non-expert.