论文标题
krylov的复杂性很大 - $ q $和双标准型SYK模型
Krylov complexity in large-$q$ and double-scaled SYK model
论文作者
论文摘要
考虑到Sachdev-Ye-Kitaev（Syk）模型的大型Q $扩展在两个阶段的限制下，我们计算了兰开斯系数，Krylov的复杂性和较高的Krylov累积量，并以$ t/q $效果以及$ t/q $效应。 Krylov的复杂性自然描述了分布的“大小”，而较高的累积物编码了更丰富的信息。我们进一步考虑在无限温度下Syk $ _Q $的双尺度限制，其中$ q \ sim \ sqrt {n} $。在这样的限制中，我们发现，争夺时间缩小到零，而兰开斯系数差异。 Krylov复杂性的生长似乎是“超快”，以前猜想与在De Sitter空间中争夺有关。
Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The Krylov complexity naturally describes the "size" of the distribution, while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK$_q$ at infinite temperature, where $q \sim \sqrt{N}$. In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be "hyperfast", which is previously conjectured to be associated with scrambling in de Sitter space.
