▎ 摘　　要

Recent experiments on the role of electron-electron interactions in fractal Dirac systems have revealed a host of interesting effects, in particular, the unique nature of the magnetic field dependence of butterfly gaps in graphene. The novel gap structure recently observed in the integer quantum Hall effect is quite intriguing [G. L. Yu et al., Nat. Phys. 10, 525 (2014)], where one observes a suppression of the ferromagnetic state at one value of the commensurable flux but a reentrant ferromagnetic state at another. In our present work we introduce the magnetic translation symmetry in the integer quantum Hall effect regime and consider the interplay between the electron-electron interaction and the periodic potential. In this approach, we explain the underlying physical processes that can lead to such a unique behavior of the butterfly gaps as observed in that system where we invoke the spin-flip transitions in the ground state.