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)