  The Hofstadter model is a simple yet powerful Hamiltonian to study quantum
Hall physics in a lattice system, manifesting its essential topological states.
Lattice dimerization in the Hofstadter model opens an energy gap at half
filling. Here we show that even if the ensuing insulator has a Chern number
equal to zero, concomitantly a doublet of edge states appear that are pinned at
specific momenta. We demonstrate that these states are topologically protected
by inversion symmetry in specific one-dimensional cuts in momentum space,
define and calculate the corresponding invariants and identify a platform for
the experimental detection of these novel topological states.
