Takuya Kitagawa (Harvard University, USA)
"Topological characterization of periodically driven systems"

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this talk, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes, and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. One set of examples of such dynamics are provided by quantum walks, which we previously showed to realize all of the topological phases classified in 1 and 2 dimensions.
We demonstrate these principles through an example of a periodically driven two--dimensional hexagonal lattice model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.
Reference: T.Kitagawa, E.Berg, M.Rudner, E.Demler, http://arxiv.org/abs/1010.6126
See also T.Kitagawa et al, Phys.Rev. A 82, 033429 (2010)