Haldane gap in the SU(3) [3 0 0] Heisenberg chain

We calculate the Haldane gap of $\mathrm{SU}(3)$ spin $[3\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}0]$ Heisenberg model using variational uniform fully symmetric matrix product states, and find that minimal $\mathrm{\ensuremath{\Delta}}/J=0.0263$ is obtained in $[2\phantom{\rule{3.33333pt}{0ex}}1\phantom{\rule{3.33333pt}{0ex}}0]$ sector at momentum $2\ensuremath{\pi}/3$. also discuss symmetry protected topological order ground state, determine full dispersion relation elementary excitations correlation lengths system.