Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9\mathrm{/}2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_s$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_s$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_A,S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_A,S)-S(L,l_A,S-1)=1\mathrm{/}(2S+1)$ for $S>3\mathrm{/}2$ in the thermodynamic limit.