290S/290K Quantum Materials Seminar speaker Dan Borgnia (UCB) Wednesday, October 5 at 2 pm in Physics North 402

Time/Venue Wednesday, October 5 at 2 pm Pacific time in Physics North 402
 and via Zoom:
https://berkeley.zoom.us/j/99523499113pwd=REovb3pyam03WXQwbEhrU3dqNHZvdz09
Meeting ID: 995 2349 9113 Passcode: 600704
Host Joel Moore
Title Localization via Quasi-Periodic Bulk-Bulk Correspondence
Abstract Quasi-periodic systems exhibit rich spectral properties, including topological invariants, mobility edges, and localization transitions. They are one of the few examples of operators we know to have a singular continuous spectrum (a generic, but poorly understood property class of operators). I will report on a new set of tools relating quasi-periodic topology and the spectral measure for the metal-insulator transition (MIT) in the almost-Mathieu operator. By constructing quasi-periodic transfer matrix equations from the limit of rational approximate projected Green’s functions using a 2D parent Hamiltonian, we treat the metal-insulator transition like a gauge transformation and link the eigenfunction localization of the MIT to the chiral edge modes of the Hofstadter Hamiltonian. This implies 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). These results have exciting consequence in the singular continuous spectrum, including applications to the Dry Ten Martini Problem.