AI 中文总结
该研究在耦合外部浴的一维粒子数守恒随机幺正电路中，揭示了单粒子格林函数的KPZ超扩散行为，通过张量网络模拟验证了相关标度与交叉的理论预测。
AI 中文摘要
我们研究与外部浴耦合的一维粒子数守恒随机幺正电路中的单粒子格林函数 $G(x,t)=\langle \sigma^-_x(0)\sigma^+_0(t)\rangle$。对于固定的时空无序，我们认为在强噪声和弱噪声极限下，$G(x,t)$ 由随机介质中的定向波主导。我们发现归一化空间分布 $p(x,t)\propto |G(x,t)|^2$ 的游荡统计及相关自由能呈现 Kardar-Parisi-Zhang（KPZ）标度。特别地，其中心 $\langle x(t)\rangle\equiv\sum_x x\\, p(x,t)$ 在 $\mathcal{O}(t^{2/3})$ 的长度尺度上游荡，而 $-\log\sum_x |G(x,t)|^2$ 的样本间涨落标度为 $t^{1/3}$。在弱噪声 $\gamma \ll 1$ 下，向强无序不动点的交叉发生在参数上很长的时间 $\mathcal{O}(\gamma^{-3/2})$。这些预测通过数值模拟得到验证，包括中等噪声下单个电路中含噪算子动力学的张量网络模拟，以及弱噪声下保留跳跃无序的相位退火代理模拟。
英文摘要
We study the single-particle Green's function $G(x,t)=\langle σ^-_x(0)σ^+_0(t)\rangle$ in one-dimensional particle-number-conserving random unitary circuits coupled to an external bath. For fixed spacetime disorder, we argue that $G(x,t)$ is governed, in both the strong- and weak-noise limits, by directed waves in a random medium. We find Kardar-Parisi-Zhang (KPZ) scaling in the wandering statistics of the normalized spatial distribution $p(x,t)\propto |G(x,t)|^2$ and in the associated free energy. In particular, its center $\langle x(t)\rangle\equiv\sum_x x\, p(x,t)$ wanders on a length-scale $\mathcal{O}(t^{2/3})$, while sample-to-sample fluctuations of $-\log\sum_x |G(x,t)|^2$ scale as $t^{1/3}$. At weak noise $γ\ll 1$, the crossover to the strong-disorder fixed point occurs at a parametrically long time $\mathcal{O}(γ^{-3/2})$. These predictions are confirmed numerically using tensor-network simulations of the noisy operator dynamics in individual circuits at moderate noise, and of a phase-annealed proxy retaining hopping disorder at weak noise.
Comments5 pages, 2 figures (with 2 pages End Matter and 11 pages Supplemental Material)
