Exploring the phase diagram of $SU(2)_4$ strange correlator

We investigate the phase diagram of a quantum many-body system constructed via the strange correlator approach, based on the non-Abelian $SU(2)_4$ fusion category, to probe topological phase transitions. Using tensor network methods, we numerically compute the half-infinite chain entanglement entropy derived from the dominant eigenvector of the transfer matrix and map the entropy across a spherical two-dimensional parameter space. Our results reveal a phase diagram significantly more complex than previously reported, including a gapless phase consistent with a conformal field theory (CFT) of central charge $c=1$. Critical lines separating distinct phases are identified, with one such line bounding the CFT phase exhibiting a higher central charge $c=2$, indicative of an unconventional critical regime.