Classification of topological phases in periodically driven interacting systems

By D. Else, C. Nayak. 2016

179 citations recorded by the source corpus.

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 $\mathbb{Z} \rtimes G$, 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 (SPT phases) are classified by the cohomology group $H^{d+1}(\mathbb{Z} \rtimes G, \mathrm{U}(1))$. 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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8932275c414ef8ab76ad4ce9bf2670c1d09a18ba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. D. Abanin
3. Maksym Serbyn
4. T. Morimoto
5. I. Bloch
6. Andrew C. Potter
7. E. Altman
8. D. Else

In Statistical and Nonlinear Physics

1. Maksym Serbyn
2. I. Bloch
3. D. Abanin
4. E. Altman
5. Andrew C. Potter
6. D. Else
7. Ashvin Vishwanath
8. T. Morimoto

Citations in the corpus

• Colloquium : Many-body localization, thermalization, and entanglement (2018, methodology): “let us turn on the coupling V̂AB, which acts locally near the boundary. Since the system is in the MBL phase, introducing a local perturbation will only significantly affect degrees of freedom situated within the localization length ξ from the boundary.(3) Thus, we expect that the new eigenstates ca”
• Chiral floquet phases of many-body localized bosons (2016, background): “cohomology Hdþ11⁄2G × Z;Uð1Þ , where the extra factor of Z corresponds to the discrete time-translation invariance of a Floquet system [22,23].”
• Gauging spatial symmetries and the classification of topological crystalline phases (2016, background): “[64], where a similar principle was conjectured for symmetry groups containing time-translation symmetry.”
• Classification of Interacting Topological Floquet Phases in One Dimension (2016, result): “Nayak [44], whose results are consistent with our own, where they overlap.”
• Periodic table for Floquet topological insulators (2016, background): “[40] Dominic V Else and Chetan Nayak, “On the classification of topological phases in periodically driven interacting systems,” arXiv (2016), 1602.”