发表机构
Technical University of Munich; TUM School of Natural Sciences, Physics Department; Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften; Munich Center for Quantum Science and Technology (MCQST); Department of Physics and Materials Science, University of Luxembourg; Donostia International Physics Center; Department of Applied Mathematics and Theoretical Physics, University of Cambridge（慕尼黑工业大学; TUM自然科学学院物理系; 瓦尔特·迈斯纳研究所，巴伐利亚科学院; 慕尼黑量子科学与技术中心; 卢森堡大学物理与材料科学系; 圣塞巴斯蒂安国际物理中心; 剑桥大学应用数学与理论物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Krylov子空间中的信息传播，发现幂律增长Lanczos系数导致超弹道光锥，因果性约束其线性增长，并扩展至Q复杂度及自旋链映射。
AI 中文摘要
Krylov子空间方法为将任何量子初值问题建模为一维链提供了高效工具。一种时间有序路径表述，其中动力学生成器在路径之间连续分裂概率，在此类动力学子空间内产生了速度极限。对于幂律增长的Lanczos系数$b_n \sim n^\delta$，我们发现超弹道光锥，对于最大增长$\delta = 1$，光锥呈指数扩展。Krylov链中的因果性约束Lanczos系数至多线性增长。我们在$SL(2, R)$和Heisenberg Weyl代数以及多体斜场Ising模型中说明了上述有效性。此外，我们将上述界限扩展到$Q$复杂度族。最后，映射到自旋链给出了Lieb Robinson界限的类似物，并将问题开放给标准凝聚态方法。
英文摘要
Krylov subspace methods provide an efficient tool for modeling any quantum initial value problem as a one dimensional chain. A time ordered path formulation, in which the dynamical generator successively splits probability between paths, yields a speed limit within such dynamical subspaces. For power law growing Lanczos coefficients $b_n \sim n^δ$ we find super ballistic lightcones, with an exponentially spreading lightcone for maximal growth $δ= 1$. Causality in the Krylov chain constrains the Lanczos coefficients to grow at most linearly. We illustrate the validity of the above in the $SL(2, R)$ and Heisenberg Weyl algebras, and in a many body skew field Ising model. Moreover, we extend the above bound to the family of $Q$ complexities. Lastly, mapping to a spin chain gives a Lieb Robinson bound analogue and opens the problem to standard condensed matter methods.
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