  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.
