Topology and stability of anomalous Floquet insulators*

The discrete (rather than continuous) time-translation symmetry of periodically-driven "Floquet systems" gives rise to new types of intrinsically dynamical topological phases, which have no analogues in equilibrium. In this talk I will first review the novel features of topology in periodically-driven systems. I will then demonstrate the stability of the two-dimensional Anomalous Floquet Insulator (AFI) -- an interacting (periodically-driven) non-equilibrium phase that exhibits nontrivial micromotion within a driving period [1,2,3], and delocalized (thermalizing) chiral states at its boundaries. The AFI bulk is stabilized against heating by disorder-induced many-body localization (MBL). Crucially, while MBL is generically expected at high driving frequencies, the AFI (and in fact all "anomalous" phases that may arise only in periodically-driven systems) require the driving frequency to be comparable to intrinsic energy scales of the system. Nonetheless we find conditions where the AFI is stable to interactions. The analytical approach that we develop is general, and can be applied to investigate the stability of a wide variety of anomalous Floquet phases. Finally I will discuss the quantized observables that serve as topological order parameters of the AFI.

[1] P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner, Phys. Rev. X 6, 021013 (2016).
[2] F. Nathan, M. S. Rudner, N. H. Lindner, E. Berg, and G. Refael, Phys. Rev. Lett. 119, 186801 (2017).
[3] F. Nathan et al., to appear.