Corrections to Diffusion in Interacting Quantum Systems,Physical Review X

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Corrections to Diffusion in Interacting Quantum Systems
Physical Review X ( IF 11.6 ) Pub Date : 2024-08-06 , DOI: 10.1103/physrevx.14.031020
Alexios A. Michailidis _{1,

2} , Dmitry A. Abanin _{1,

3} , Luca V. Delacrétaz _{1,

4,

4}

Affiliation

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor ⟨n(x,t)n⟩, in the presence of a single U(1) or SU(2) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems.

Published by the American Physical Society

2024

中文翻译：

相互作用量子系统中的扩散校正

在相互作用的经典系统和量子系统中实现平衡的方法是一个具有理论和实验兴趣的具有挑战性的问题。表征平衡的一个有用的组织原则是耗散普遍性类，最普遍的是扩散。在本文中，我们使用扩散的有效场论（EFT）系统地获得对扩散的通用幂律校正。然后，我们采用经典系统和量子系统的大规模模拟来探索它们的有效性。特别是，在具有和不具有粒子-空穴对称性的系统中，当存在单个 U（1）或 SU（2）电荷时，我们发现了用于修正动力学结构因子 ⟨n（x，t）n⟩ 的通用缩放函数，并提出了将计算推广到多个电荷的框架。经典模拟显示与 EFT 预测对次导校正的显着一致性，将热化系统有效理论的精确测试推向了前所未有的水平。转向量子系统，我们在具有守恒磁化强度的幺正和噪声 1D Floquet 系统中执行大规模张量网络模拟。我们发现与 EFT 有定性一致，在嘈杂系统的情况下，它变得定量。此外，我们还展示了 EFT 校正知识如何允许拟合方法，这可以改进模拟和实验可访问的中间时间的传输参数估计。最后，我们探讨了量子系统中的非线性响应，发现 EFT 为其行为提供了准确的预测。我们的结果为更好地理解热化系统中存在的非线性现象提供了基础。美国物理学会 2024 年出版

更新日期：2024-08-06

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