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Quantum Matter Seminar

Monday, February 14, 2022
4:00pm to 5:00pm
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East Bridge 114
Quasi-Periodic Topological Bulk-Bulk Correspondence and the Dry Ten Martini Problem
Dan Borgnia, Physics: Quantum Condensed Matter, Harvard University,

QM Seminar *In person*

We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal-insulator transition. By constructing quasi-periodic transfer matrix equations from the limit of rational approximate projected Green's functions, we reduce results from SL(2,R) co-cycle theory (transfer matrix eigenvalue scaling) to consequences of translation invariant band theory. This reduction links the eigenfunction localization of the metal-insulator transition to the chiral edge modes of the Hofstadter Hamiltonian. Our analysis shows the localized phase roots in a topological "bulk-bulk" correspondence rather than self-duality, differentiating quasi-periodic localization from Anderson localization in disordered systems. These results and methods are widely relevant to systems beyond this paradigmatic model, including 2D cold atom realizations, and have direct application to Barry Simon's "Dry Ten Martini Problem" at criticality.

For more information, please contact Loly Ekmekjian by phone at x 4314 or by email at [email protected].