发表机构
Saha Institute of Nuclear Physics; Homi Bhabha National Institute; Instituto de Física Teórica UAM/CSIC; Universidad Autónoma de Madrid（萨哈核物理研究所; 霍米·巴巴国立研究所; 马德里自治大学/西班牙国家科学研究委员会理论物理研究所; 马德里自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有限维混沌量子多体系统，提出对称分辨Krylov复杂度的晚期维数加权均分规则，经多种模型数值验证，明确分辨精确对称性对Krylov复杂度诊断混沌算符增长的关键作用。
AI 中文摘要
我们研究有限维混沌量子多体系统中的对称分辨Krylov复杂度。当哈密顿量和初始算符均与一个守恒荷对易时，算符动力学可分解为独立的对称 sector，每个 sector 有其自身的Krylov链。我们证明，饱和后，未分辨的Krylov复杂度在各对称 sector 上是可加的。在无额外Liouvillian简并的情况下，希尔伯特空间维数为$d_q$的sector的晚期贡献由$d_q(d_q-1)$控制，导致维数加权均分，其趋近于简单的大sector标度$d_q^2/\bigcup_{q'}d_{q'}^2$。这一晚期规则与文献中讨论的早期加权平均不同，而是由可访问算符空间的维数决定。我们通过实SYK模型、复SYK模型、混沌玻色自旋模型和混合场伊辛链的数值研究验证了该解析预测。我们的结果表明，分辨精确对称性对将Krylov复杂度的饱和值解释为混沌算符增长的诊断量至关重要。
英文摘要
We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension $d_q$ is controlled by $d_q(d_q-1)$, leading to a dimension-weighted equipartition that approaches the simple large-sector scaling $d_q^2/\sum_{q'}d_{q'}^2$. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.
Commentsv1: 38 pages, 7 figures. v2: references added
