Realization of strongly interacting topological phases on lattices
Antoine Sterdyniak, Universität Innsbruck
While fractional quantum Hall effect (FQHE) was realized experimentally thirty years ago in semiconductor heterostructures, strongly interacting chiral topological phases are still at the center of an important research effort, both as they serve as building blocks of more exotic phases such as fractional topological insulators and as a realization outside of semi-conductor physics is still missing. In this talk, I will describe realizations of these phases in cold atoms gases and in frustrated spins systems. I will first introduce optical flux lattices, which are continuous models that exhibit topological flat bands with a tunable Chern number and host fractional states beyond the FQHE. Then, I will focus on chiral spin liquids whose emergence on the kagomé lattice using local Hamiltonians has been shown very recently. Unlike itinerant particle systems where FQHE can be understood as a consequence of interactions in a partially filled topological band, I will show that such a picture does not hold for this chiral spin liquid. However, it can be described by model states obtained using a slave boson approach.