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

摘要

One-dimensional tight binding models such as the Aubry-Andre-Harper (AAH) model (with an on-site cosine potential) and the integrable Maryland model (with an on-site tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two-dimensional (2D) Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, such a connection needs to be made for the Maryland model (MM). Here 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 one-dimensional MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.