Localization via Quasi-Periodic Bulk-Bulk Correspondence
Abstract
We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing quasi-periodic transfer matrix equations from the limit of rational approximate projected Green's functions, we relate results from co-cycle theory (transfer matrix eigenvalue scaling) to consequences of rational band theory. This reduction links the eigenfunction localization of the MIT to the chiral edge modes of the Hofstadter Hamiltonian, implying the localized phase roots in a topological "bulk-bulk" correspondence, a bulk-boundary correspondence between the 1D AAH system (boundary) and its 2D parent Hamiltonian (bulk). This differentiates quasi-periodic localization from Anderson localization in disordered systems. Our results are widely applicable to systems beyond this paradigmatic model.
Cite
@article{arxiv.2111.02789,
title = {Localization via Quasi-Periodic Bulk-Bulk Correspondence},
author = {Dan S. Borgnia and Robert-Jan Slager},
journal= {arXiv preprint arXiv:2111.02789},
year = {2023}
}
Comments
6+12 pages, 2+2 figures, 1 table. Companion paper to arXiv:2109.13933 concerning different themes and new results. Supplementary materials shared with arXiv:2109.13933, but kept for readability and completeness. arXiv admin note: substantial text overlap with arXiv:2109.13933