Abstract:
The mean-field theory and simulation result of the easy-plane
t-
λ model and the mean-field phase diagram are given in this paper. Two mean-field scenarios exist for doping the pure QSH state: 1) a first-order QSH-SSC transition occurs in the weak interaction region; 2) a continuous QSH to QSH-SSC co-existence transition followed by a first-order QSH-vanishing transition in the strong interaction region. The mean-field theory is found to capture features for symmetry-broken phases but give the wrong conclusion of QSH-SSC co-existence due to ignoring fluctuation. It is unable to characterize transitions with topological excitation.