Abstract
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry . We argue for a general correspondence between such phases and topological phases of undriven systems protected by symmetry where the additional accounts for the discrete time-translation symmetry. Thus, for example, the bosonic phases in spatial dimensions without intrinsic topological order [symmetry-protected topological (SPT) phases] are classified by the cohomology group . For unitary symmetries, we interpret the additional resulting Floquet phases in terms of the lower-dimensional SPT phases that are pumped to the boundary during one time step. These results also imply the existence of novel symmetry-enriched topological (SET) orders protected solely by the periodicity of the drive.
- Received 25 March 2016
- Revised 20 April 2016
DOI:https://doi.org/10.1103/PhysRevB.93.201103
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