Floquet Topological Order in Interacting Systems of Bosons and Fermions

Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous charge and information transport at the boundary. Drives of this form are applicable to generic systems of bosons, fermions, and spins, and may be characterized by the anomalous unitary operator that acts at the edge of an open system. We find that these operators are robust to all local perturbations and may be classified by a pair of coprime integers. This defines a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals.

Figure 1

(a) Four steps in the anomalous Floquet drives considered in the main text, based on the model of Ref. [9]. (b) Representation of the action of the complete unitary drive. See main text for details.

Figure 2

(a) Permutation of boson occupation numbers at the edge under the anomalous Floquet drive. (b) Action of the putative open 1D unitary ${\tilde{U}}_{\text{op}}^B$. The regions marked $L$ and $R$ are within a distance $v_{LR}T$ of the cut. See main text for details.

Figure 3

(a) Permutation of on-site states under the action of ${\tilde{U}}_{\text{op}}^{\leftrightarrow }$, assuming the 1D chain is cut between sites $L$ and $-L$. (b) Relabeling of lattice sites so that the permutation is diagonal away from the cut.