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 Néel 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)-Néel order parameter vanishes. The fermionic bilinear order parameter is instead a biadjoint with respect to SO(3); unlike its Néel cousin, it constitutes an interaction-induced insulator. Furthermore, I show that the Néel 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 Néel transition opens the possibility of posing further constraints on spinon properties from thermodynamic measurements near criticality alone.

中文翻译：

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非常规 Gross-Neveu 量子临界性：相互作用引起的 SO(3)-双共绝缘体和涌现的 SU(3) 对称性

我指出，在三个时空维度上具有 SO(3) 同位旋的 Gross-Neveu 理论（例如，最近提出的，作为对某些自旋轨道液体中的尼尔跃迁的有效描述）也具有更奇特的量子临界性种类。有序相自发破坏 SO(3)，但 SO(3)-Néel 有序参数消失。费米子双线性阶参数是相对于 SO(3) 的双共轭；与它的表亲尼尔不同，它构成了一种相互作用引起的绝缘体。此外，我还证明了 Néel 和双共轭阶参数可以组合起来变换为 SU(3) 对称性下的共轭；对称性出现在分离对称半金属和双邻绝缘体的临界点，但前提是风味数足够小，这表明有序参数波动和不同通道之间的相互作用在稳定扩大对称性方面发挥着至关重要的作用。在候选 SO(3) 自旋轨道液体中，热力学临界指数带有“自旋子”的指纹。除了尼尔转变之外，独立普适性类别的存在开启了通过仅接近临界点的热力学测量对自旋子性质施加进一步限制的可能性。