Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry

I point out that Gross-Neveu theory with SO(3) isospin in three space-time dimensions---proposed recently, for instance, as an effective description of the N\'eel transition in certain spin-orbital liquids---also hosts quantum criticality of a more exotic kind. The ordered phase breaks SO(3) spontaneously, but the SO(3)-N\'eel order parameter vanishes. The fermionic bilinear order parameter is instead a biadjoint with respect to SO(3); unlike its N\'eel cousin, it constitutes an interaction-induced insulator. Furthermore, I show that the N\'eel and biadjoint order parameters can be combined to transform as an adjoint under SU(3) symmetry; the symmetry is emergent at the critical point separating the symmetric semimetal and the biadjoint insulator, but only if the flavor number is small enough, suggesting order-parameter fluctuations and the interplay between different channels play a crucial role in stabilizing the enlarged symmetry. In candidate SO(3) spin-orbital liqiuds, thermodynamic critical exponents carry fingerprints of ``spinons.'' The existence of an independent universality class in addition to the N\'eel transition opens the possibility of posing further constraints on spinon properties from thermodynamic measurements near criticality alone.