Year: 2016
Type: article
Abstract: We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems protected by symmetry $\mathbb{Z}\ensuremath{\rtimes}G$ where the additional $\mathbb{Z}$ accounts for the discrete time-translation symmetry. Thus, for example, the bosonic phases in $d$ spatial dimensions without intrinsic topological order [symmetry-protected topological (SPT) phases] are classified by the cohomology group ${H}^{d+1}[\mathbb{Z}\ensuremath{\rtimes}G,\mathrm{U}(1)]$. 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.
Authors: Dominic V. Else, Chetan Nayak
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2273662557