Abstract: Topological insulators constitute a different phase of quantum matter from ordinary insulators, despite not breaking any symmetries. They are an example of a 'symmetry protected topological' phase, in that they exhibit exotic phenomena, namely gapless surface modes, that are entirely protected by time reversal symmetry. Motivated by this, one can classify all possible non-trivial topological insulators in all dimensions and symmetry classes at the level of band structures. However, the role of interactions in this scheme is still not completely understood. In this talk, I'll describe our recent work on classifying interacting analogues of topological insulators, and constructing exactly solvable lattice realizations of them, which may allow them to be targeted by numberical algorithms.
