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We numerically demonstrate that, although it is critical, the two-boxsymmetric $\mathrm{SU}(3)$ chain possesses edge states in the adjointrepresentation whose excitation energy scales with the number of sites $N_s$ as$1/(N_s \log N_s)$, in close analogy to those found in half-integer$\mathrm{SU}(2)$ chains with spin $S\ge 3/2$. We further show that these edgestates dominate the entanglement entropy of finite chains, explaining why ithas been impossible so far to verify with DMRG simulations the field theoryprediction that this model is in the $\mathrm{SU}(3)_1$ universality class.Finally, we show that these edge states are very efficiently screened byattaching adjoint representations at the ends of the chain, leading to anestimate of the central charge consistent within 1\% with the prediction $c=2$for $\mathrm{SU}(3)_1$.

Edge states and universality class of the critical two-box symmetric SU(3) chain