Density-matrix renormalization-group simulation of the $\mathit{SU}\left(3\right)$ antiferromagnetic Heisenberg model

We analyze the antiferromagnetic $\mathit{SU}\left(3\right)$ Heisenberg chain by means of the density-matrix renormalization group. The results confirm that the model is critical and the computation of its central charge and the scaling dimensions of the first-excited states show that the underlying low-energy conformal field theory is the $\mathit{SU}{\left(3\right)}_1$ Wess-Zumino-Novikov-Witten model.

Figure 1

(Color online) Plot of the ground state $E_{00}$ and first-excited states for chains of different lengths (from $L=12$ up to $L=52$). The solid lines correspond to scaling dimensions $\frac{1}{3}$ and $\frac{2}{3}$ and have been drawn as a guide for the eye. For sake of clarity, not all the degeneracies have been reported.

Figure 2

(Color online) Analysis of the von Neumann entropy using 2000 DMRG states. The figure on the left (a) shows $S_n$ as a function of the block length $n$ for different sizes $L$ of the chain; the figure on the right (b) is the plot of the same data fitted in a logarithmic scale. The linear fit of these data provides the value for the central charge $c=1.995\pm 0.001$.