AI 中文总结
研究算符乱序有效动力学背后对称原理，基于强到弱U(1)对称性破缺发展有效场论，用四重Keldysh轮廓表示OTOC，受对偶性约束，由有噪声的FKPP方程控制动力学，揭示算符大小流体动力学和乱序的对称起源。
AI 中文摘要
算符乱序通常通过非时序关联函数（OTOCs）的增长来诊断，但其有效动力学背后的一般对称原理仍不清楚。对于布朗或短时间相关的大N马约拉纳系统，我们发展了一种基于对称的算符乱序有效场论，由算符空间中从强到弱的U(1)对称性破缺组织。关键观察是，在非相互作用费米子极限下，OTOC的四重Keldysh轮廓表示在加倍的希尔伯特空间描述中允许出现强U(1)对称性。我们进一步表明，高阶对称性破缺项受到时间反演与轮廓置换相结合的对偶性的严格约束。由此产生的OTOC动力学由一个有噪声的FKPP方程控制，该方程在统一框架内捕捉了算符乱序的早期指数增长、弹道传播、非线性饱和和随机前沿展宽。我们在布朗SYK链中验证了这种构造。我们的结果揭示了算符大小流体动力学和乱序的对称起源。
英文摘要
Operator scrambling is commonly diagnosed by the growth of out-of-time-ordered correlators (OTOCs), yet a general symmetry principle underlying their effective dynamics has remained elusive. For Brownian or short-time-correlated large-$N$ Majorana systems, we develop a symmetry-based effective field theory for operator scrambling, organized by a strong-to-weak U(1) symmetry breaking in operator space. The key observation is that, in the noninteracting fermion limit, the four-fold Keldysh contour representation of an OTOC admits an emergent strong U(1) symmetry in a doubled Hilbert-space description, even when the original system has no ordinary conserved quantity. The associated slow mode is the phase of the strong-charge creation operator, whose conjugate density is identified with the local operator size. Generic interactions explicitly break the strong symmetry and generate a mass term at lowest order for the would-be Goldstone mode, thereby converting diffusive operator spreading into chaotic growth. We further show that higher-order symmetry breaking terms are tightly constrained by an emergent duality that combines time reversal with contour permutation. This duality fixes the effective action up to quadratic order in the response field, relates the multiplicative noise strength directly to the Lyapunov exponent, and makes the positivity of the Lyapunov exponent a consequence of convergence of the real-time path integral. The resulting OTOC dynamics is governed by a noisy FKPP equation, which captures within a unified framework the early-time exponential growth, ballistic propagation, nonlinear saturation, and stochastic front broadening of operator scrambling. We verify this construction in a Brownian SYK chain, where a direct saddle-point expansion reproduces the symmetry-based effective action. Our results reveal a symmetry origin of operator-size hydrodynamics and scrambling.
Comments32 pages main text + 16 pages appendix, 7 figures
