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

TL;DR

This paper numerically investigates the critical two-box symmetric SU(3) chain, revealing edge states with unique scaling, their influence on entanglement entropy, and confirming the model's universality class as SU(3)_1.

Contribution

It demonstrates the existence and scaling of edge states in the SU(3) chain and confirms its universality class through entanglement entropy analysis.

Findings

Edge states scale as 1/(N_s log N_s)

Edge states dominate entanglement entropy

Estimated central charge c≈2 for SU(3)_1

Abstract

We numerically demonstrate that, although it is critical, the two-box symmetric $\mathrm{SU}(3)$ chain possesses edge states in the adjoint representation 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 edge states dominate the entanglement entropy of finite chains, explaining why it has been impossible so far to verify with DMRG simulations the field theory prediction that this model is in the $\mathrm{SU}(3)_1$ universality class. Finally, we show that these edge states are very efficiently screened by attaching adjoint representations at the ends of the chain, leading to an estimate of the central charge consistent within 1\% with the prediction $c=2$ for $\mathrm{SU}(3)_1$.