Finite Temperature Phase Diagram in Rotating Bosonic Optical Lattice
  Finite temperature phase boundary between superfluid phase and normal state is analytically derived by studying the stability of normal state in rotating bosonic optical lattice. We also prove that the oscillation behavior of critical hopping matrix directly follows the upper boundary of Hofstadter butterfly as the function of effective magnetic field. 
Beibing Huang, Shaolong Wan