多体局域化动力学的稳定性与准周期性
Stability and quasi-Periodicity of Many-Body Localized Dynamics
AI总结：
本文通过证明无序海森堡链中子系统纠缠演化在热力学极限下保持稳定准周期性，为多体局域化动力学稳定性提供了具体证据，并指出先前报道的对数增长源于被禁止的系综平均。
摘要：
孤立多体量子系统中纠缠动力学与非平衡统计之间的联系已在理论和实验上得到确立。多体局域化（MBL）——无序（即随机）链中相互作用粒子无法热化的现象——体现了这种联系。然而，由于缺乏分析多体纠缠动力学的稳健方法，对MBL等临界现象的系统性证明仍然具有挑战性。在本文中，我们通过无序海森堡链子系统纠缠演化中的准周期动力学来识别MBL。这种通过纠缠的稳定准周期动力学——其中“稳定”意味着它们在热力学极限下持续存在——来刻画MBL的新形式，具体区分了两种相互竞争的图景：子系统的完全局域化行为，或子系统以指数级缓慢（随无序强度）的方式热化——这是文献中一个激烈争论的问题。利用微扰理论，我们通过无穷微扰级数推导出单自旋的纠缠动力学，同时对稀有Griffiths区域（局部热化夹杂）进行建模。我们的结果证明，在足够强无序的区域内，单个子系统的纠缠演化在热力学极限下保持准周期性，从而为无序海森堡链中MBL动力学的稳定性提供了具体证据。这种行为与文献中广泛报道的MBL相中子系统纠缠的对数增长形成对比。我们表明，先前研究中观察到的对数增长源于统计系综平均，而由于MBL系统固有的非遍历动力学特性（根植于其准周期特征），这种平均是被禁止的。
英文摘要：
The connection between entanglement dynamics and non-equilibrium statistics in isolated many-body quantum systems has been established both theoretically and experimentally. Many-Body Localization (MBL), a phenomenon where interacting particles in disordered (i.e., random) chains fail to thermalize, exemplifies this connection. However, the systematic proof of critical phenomena such as MBL remains challenging due to the lack of robust methods for analyzing many-body entanglement dynamics. In this paper, we identify MBL through quasi-periodic dynamics in the entanglement evolution of subsystems in a disordered Heisenberg chain. This new form of characterizing MBL, through stable quasi-periodic dynamics of entanglement -- where stable means they persist in the thermodynamic limit -- concretely distinguishes between two competing scenarios: fully localized behavior of subsystems or slowly, exponentially slow in disorder, thermalizing subsystems -- a heated controversy in the literature. Utilizing perturbation theory, we derive the entanglement dynamics of single spins through an infinite perturbative series, while also modeling rare Griffiths regions (locally thermal inclusions). Our results prove that in regimes of sufficiently strong disorder, the entanglement evolution of individual subsystems remains quasi-periodic in the thermodynamic limit, thereby providing concrete evidence for the stability of MBL dynamics in disordered Heisenberg chains. This behavior contrasts with the widely reported logarithmic growth of subsystem entanglement in the MBL phase. We show that the logarithmic growth observed in prior studies arises from statistical ensemble averaging, which is prohibited due to the intrinsic non-ergodic dynamics characteristic of MBL systems, rooted in their quasi-periodic features.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
