Quasi-Periodic Bulk-Boundary Correspondence and the 1D Metal-Insulator Transition
ORAL
Abstract
The regime of strong aperiodicity is not frequently discussed in the context of topological materials. Aiming to better understand such systems, this work generalizes results from translation-invariant systems to their aperiodic counterparts. We connect bulk-boundary correspondence and the gap-labeling theorem to the dynamics of quasi-periodic eigenfunctions. Focusing on the almost-Matthieu operator (Andre-Aubry-Harper model) and its 1D Metal-Insulator Transition (MIT), we provide a novel approach to Barry Simon's "Dry Ten Martini" problem in the singularly continuous regime. Further applications of this formalism are discussed, including the generalization to other quasi-periodic models and the breakdown of bulk-boundary correspondence in quasi-crystals.
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Presenters
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Dan Borgnia
Harvard University
Authors
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Dan Borgnia
Harvard University
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Robert-Jan Slager
University of Cambridge, TCM Group, Cavendish Laboratory, University of Cambridge, TCM Group, Cavendish Laboratory/ Department of Physics, University of Cambridge/ Harvard University, Harvard University
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Ashvin Vishwanath
Harvard University, Department of Physics, Harvard University, Department of Physics and Astronomy, Harvard University, Department of Physics, Harvard university