We provide evidence for the mapping of critical spin-1 chains, in particular the $\mathrm{SU}\left(3\right)$ symmetric bilinear-biquadratic model with additional interactions, to free boson theories using exact diagonalization and the density-matrix renormalization-group algorithm. Using the correspondence with a conformal field theory with central charge $c=2$, we determine the analytic formulas for the scaling dimensions in terms of four Tomonaga-Luttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these field-theoretic parameters and track their evolution as a function of the parameters of the lattice model.

• Received 15 February 2015
• Revised 17 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075128