Topological Phase Transition in the Hofstadter-Hubbard Model
  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. 
Lei Wang, Hsiang-Hsuan Hung and Matthias Troyer
cond-mat.str-el cond-mat.quant-gas cond-mat.supr-con