Global quantum correlations in the spin-1 bilinear-biquadratic chain

We investigate global properties of the ground state of the spin-1 bilinear-biquadratic quantum spin chain in the thermodynamic limit, focusing on the geometric entanglement and fidelity diagram. The two quantities are computed via iTEBD and they appear to be capable of detecting the various well-known phase transitions in the system, including a Kosterlitz-Thouless one. The two quantities also behave distinctively at other points in the phase diagram. In particular, this is the case for the fidelity diagram at $\theta \approx 1.34 \pi$ (around a possible transition to a spin nematic phase), and also for the geometric entanglement at the integrable gapped point $\theta = 3 \pi /2$, where we conjecture an infinite entanglement length in the system.