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Topological characterization of periodically driven quantum systems

Takuya Kitagawa, Erez Berg, Mark Rudner, and Eugene Demler
Phys. Rev. B 82, 235114 – Published 10 December 2010

Abstract

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two-dimensional hexagonal lattice tight-binding model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.

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  • Received 29 October 2010

DOI:https://doi.org/10.1103/PhysRevB.82.235114

©2010 American Physical Society

Authors & Affiliations

Takuya Kitagawa, Erez Berg, Mark Rudner, and Eugene Demler

  • Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 82, Iss. 23 — 15 December 2010

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