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The Dry Ten Martini Problem at Criticality
Dan S. Borgnia, Robert-Jan Slager, Matthew Faust
We solve the dry ten martini problem (lean-verified this time) by showing that every labeled almost Mathieu gap is open for and every irrational frequency. In particular,…
Localization via Quasi-Periodic Bulk-Bulk Correspondence
Dan S. Borgnia, Robert-Jan Slager
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 matr…
Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
Dan S. Borgnia, Ashvin Vishwanath, Robert-Jan Slager
We introduce the projected Green's function technique to study quasi-periodic systems such as the Andre-Aubry-Harper (AAH) model and beyond. In particular, we use projected Green's…