Figure 3.

(a–c) Spectra on the critical line ${\lambda }_2=-\mu$ (with $\mu =1$). There are two gapless points around which the spectra is linear (i.e., $E_k\propto k$) which implies $z=1$. (d) Spectra at multi-critical point with ${\lambda }_1=2\mu$ and ${\lambda }_2=-\mu$. Two gapless points confluence at $k=0$ where the spectra is quadratic (i.e., $E_k\propto k^2$) and $z=2$.