Effective Field Theory for the $\mathrm{SO}(n)$ Bilinear-Biquadratic Spin Chain

We present a low-energy effective field theory to describe the $\mathrm{SO}(n)$ bilinear-biquadratic spin chain. We start with $n=6$ and construct the effective theory by using six Majorana fermions. After determining various correlation functions, we characterize the phases and establish the relation between the effective theories for SO(6) and SO(5). Together with the known results for $n=3$ and 4, a reduction mechanism is proposed to understand the ground state for arbitrary $\mathrm{SO}(n)$. Also, we provide a generalization of the Lieb-Schultz-Mattis theorem for $\mathrm{SO}(n)$. The implications of our results for entanglement and correlation functions are discussed.

Figure 1

Predicted phase diagram of the SO(6) bilinear-biquadratic spin chain in Ref. 8. The shaded area is the region considered in this Letter.