Figure 1

Topological phase diagram of model Hamiltonian for \(\mu =1\). Line ‘ac’ represents the critical line \( \lambda _2=\mu -\lambda _1 \) (blue line), line ‘be’ represents the critical line \(\lambda _2=-\mu \) (magenta line) and line ‘ad’ represents the critical line \(\lambda _2=\mu +\lambda _1\) (red line). Points ‘a’ and ‘b’ are multi-critical points (green and black dots respectively) which differentiate between three distinct gapped phases with \(w=0,1,2\) (represented in different colors). Here CP-1 is critical/gapless phase for the transition between \(w=0\) and \(w=1\). CP-2 is critical/gapless phase for the transition between \(w=1\) and \(w=2\).