  We study the interplay between topological and conventional long range order
of attractive fermions in a time reversal symmetric Hofstadter lattice using
quantum Monte Carlo simulations, focussing on the case of one-third flux
quantum per plaquette. At half-filling, the system is unstable towards s-wave
pairing and charge-density-wave order at infinitesimally small interactions. At
one-third-filling, the noninteracting system is a topological insulator, and a
nonzero critical interaction strength is needed to drive a transition from the
quantum spin Hall insulator to a superfluid. We probe the topological signature
of the phase transition by threading a magnetic flux through a cylinder and
observe quantized topological charge pumping.
