Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point

Abstract

One dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two dimensional Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, no such connection has been made for the Maryland model (MM). In this work, we describe a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the 1D MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.