AI 中文总结
该研究构建SO(2)×O(N)非平衡非线性σ模型，将KPZ物理扩展至非阿贝尔对称性，揭示低维下非热不动点与非常规弱动态标度，为非阿贝尔时间晶体研究提供理论支撑。
AI 中文摘要
我们识别出一类由连续对称性破缺与弱非平衡驱动相互作用产生的宽泛非热相。将 Kardar-Parisi-Zhang（KPZ）物理扩展至与周期性时间平移破缺相关的单一SO(2)时间子（chronon）之外，我们构建了适用于SO(2)×O(N)对称性的非平衡非线性σ模型，描述兼具时间与内部序的非阿贝尔时间晶体。这种对称性结构在驱动型量子材料、活性物质及光诱导周期态中自然产生。针对旋转相与振荡相，我们推导了戈德斯通理论，表明在有序 regime 深处，时间子-O(N)耦合仍保持有限。单圈重整化群分析揭示了类似KPZ的维数结构：在d=1、2时，任意弱非平衡微扰都会使平衡不动点失稳，生成强耦合非热不动点，实现涌现平衡破缺；相比之下，当d>2时，弱微扰无关紧要，有效平衡得以恢复。核心结果是旋转相中的非常规弱动态标度：尽管属于同一序参量，强耦合戈德斯通扇区仍呈现出不同的普适动力学指数。我们通过解析方法表征该标度，并在1+1维中通过直接模拟予以验证。在振荡相中，我们重现并扩展了漂移聚合物中已知的弱标度 regime。最后，紧致性与拓扑缺陷最终会破坏长程序，但留下可实验观测的非热标度窗口。综上，这些结果将KPZ普适性扩展至非阿贝尔对称性破缺领域。
英文摘要
We identify a broad class of nonthermal phases generated by the interplay of continuous symmetry breaking and weak nonequilibrium driving. Extending Kardar-Parisi-Zhang (KPZ) physics beyond the single $SO(2)$ chronon associated with periodically broken time translations, we construct nonequilibrium nonlinear sigma models for $SO(2)\times O(N)$ symmetry, describing non-Abelian time crystals with coexisting temporal and internal order. This symmetry structure arises naturally in driven quantum materials, active matter, and optically induced periodic states. For rotating and oscillating phases, we derive the Goldstone theories and show that chronon-$O(N)$ couplings remain finite deep in the ordered regime. One-loop renormalization group analysis reveals a KPZ-like dimensional structure: in $d=1,2$, arbitrarily weak nonequilibrium perturbations destabilize the equilibrium fixed point and generate strongly coupled nonthermal fixed points, realizing emergent equilibrium breaking. By contrast, for $d > 2$, weak perturbations are irrelevant and effective equilibrium is restored. A central result is unconventional weak dynamic scaling in the rotating phase: strongly coupled Goldstone sectors acquire distinct universal dynamical exponents despite belonging to the same order parameter. We characterize this scaling analytically and corroborate it through direct simulations in $1+1$ dimensions. In the oscillating phase, we recover and extend weak-scaling regimes known from drifting polymers. Finally, compactness and topological defects ultimately destroy long-range order but leave experimentally accessible nonthermal scaling windows. Together, these results extend KPZ universality to non-Abelian symmetry breaking.
