The phase diagram of the model. The phase boundary in which the gap closes are obtained from Z(0) = 0 and Z(π/2a) = 0. The parameters are chosen as: (a) t_A = 0, t_B = 0; (b) t_A = 0.1t, t_B = −0.1t; (c) t_A = 0.5t, t_B = 0.5t; (d) t_A = 1.25t, t_B = 0.8t, respectively. The change of phase transformation points which is caused by the NNN hopping can be described by a shift of chemical potential.