论文标题
量子场理论中的Krylov复杂性
Krylov complexity in quantum field theory, and beyond
论文作者
论文摘要
我们研究了各种量子场理论模型中的Krylov复杂性：扁平空间和球体，全息模型和带有UV-Cutoff的晶格模型上的自由大规模玻色子和费米子。在某些情况下，我们发现兰开斯系数的渐近行为超出了以前观察到的普遍性。我们确认，在所有情况下，Krylov复杂性的指数增长都满足了猜想的不平等，这概括了Maldacena-Shenker-Stanford陷入混乱。我们讨论了兰开斯系数的温度依赖性，并注意到，兰开斯系数和混乱的生长之间的关系只能适用于在UV临界值下由物理学控制的足够晚期，真正的渐近状态。与以前的建议相反，我们显示了量子场理论中的Krylov复杂性在质量上与全息复杂性不同的情况。
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of Lanczos coefficients, which goes beyond previously observed universality. We confirm that in all cases the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of Lanczos coefficients and note that the relation between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime governed by the physics at the UV cutoff. Contrary to previous suggestions, we show scenarios when Krylov complexity in quantum field theory behaves qualitatively differently from the holographic complexity.
