Effective vacua for Floquet topological phases: A numerical perspective on the switch-function formalism
Abstract
We propose a general edge index definition for two-dimensional Floquet topological phases based on a switch-function formalism. When the Floquet operator has a spectral gap, the index covers both clean and disordered phases, anomalous or not, and does not require the bulk to be fully localized. It is interpreted as a nonadiabatic charge pumping that is quantized when the sample is placed next to an effective vacuum. This vacuum is gap-dependent and obtained from a Floquet Hamiltonian. The choice of a vacuum provides a simple and alternative gap-selection mechanism. Inspired by the model from Rudner et al. we then illustrate these concepts on Floquet disordered phases. Switch-function formalism is usually restricted to infinite samples in the thermodynamic limit. Here we circumvent this issue and propose a numerical implementation of the edge index that could be adapted to any bulk or edge index expressed in terms of switch functions, already existing for many topological phases.
- Publication:
-
Physical Review B
- Pub Date:
- May 2018
- DOI:
- 10.1103/PhysRevB.97.195312
- arXiv:
- arXiv:1801.08807
- Bibcode:
- 2018PhRvB..97s5312T
- Keywords:
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- Condensed Matter - Mesoscale and Nanoscale Physics;
- Mathematical Physics
- E-Print:
- 13 pages, 10 figures, Correcting some typos and including an application to a non-anomalous model. To appear in Physical Review B