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arXiv 2602.09098cond-mat.stat-mechquant-ph
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可积随机量子电路中的异常自旋输运

Anomalous spin transport in integrable random quantum circuits

School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）

Songlei Wang, Chenguang Liang, Hongzheng Zhao, Zhi-Cheng Yang

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26 pages,16 figures
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AI总结：

本文研究了可积随机量子电路中自旋输运的异常行为，通过构建非均匀XXZ R矩阵电路，揭示了弹道、超扩散和扩散区域的相图，并发展了广义流体动力学框架以预测输运特性。

摘要：

高温下可积量子自旋链的自旋输运表现出丰富的动态相图，包括弹道、超扩散和扩散区域。尽管可积性已知在静态和周期驱动系统中得以保持，但在完全缺乏时间平移对称性的系统中，特别是相互作用随机量子电路中，其命运仍不清楚。本文构建了由非均匀XXZ R矩阵组成的可积随机量子电路。令人惊讶的是，无论门层序列是准周期性还是完全随机，可积性都得以保持，从而显式地破坏了连续和离散的时间平移对称性。利用无限温度和半填充下的大规模时间依赖密度矩阵重整化群模拟，我们绘制出由此产生的自旋输运相图，并识别出由R矩阵的谱参数控制的弹道、超扩散和扩散区域。每个区域内的自旋相关结构在时间和空间上都对非均匀性敏感，表现出空间不对称性和与近退化准粒子速度相关的尖峰结构。为了解释这些发现，我们开发了一种适用于时间依赖可积电路的广义流体动力学框架，从而得到相关函数、Drude权重和扩散界限的欧拉尺度预测。该方法识别了支配输运的准粒子，并定量捕捉了数值观察到的相关轮廓的标度指数和精细结构。我们的结果表明，精确的Yang-Baxter可积性与随机量子动力学是兼容的，并建立了广义流体动力学作为时间依赖可积系统输运的预测框架。

英文摘要：

High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.

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