  We study critical phenomena of the SU(3) symmetric spin-1 chains when adding
the SU(3) asymmetric term. To investigate such system, we numerically
diagonalize the Dimer-Trimer (DT) model Hamiltonian around the SU(3) symmetric
point, named the pure trimer (PT) point. We analyze our numerical results with
the conformal field theory (CFT). First of all, we discover soft modes at the
wave number q = 0 and q = 2{\pi}/3 for the PT point, and then the system is
critical. Secondly, we find that the system at the PT point belongs to the CFT
with the central charge c = 2 and the scaling dimension x = 2/3. Finally, by
investigating the eigenvalues of the Hamiltonian in the vicinity of the PT
point, we find that there is a phase transition at the PT point from a massive
phase to a massless phase. From these numerical results, the phase transition
at the PT point belongs to the Berezinskii-Kosterlitz-Thouless (BKT)-like
universality class that is explained by the level-1 SU(3) Wess-Zumino-Witten
(SU(3) 1 WZW) model.
