Title: Multiseed Krylov complexity Show Chinese title

Title: 多种子Krylov复杂性

Abstract: Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and chaotic dynamics, but its ability to do so depends precariously on the choice of the initial seed. We propose to apply such considerations not to a single operator, but simultaneously to a collection of initial seeds in the manner of the block Lanczos algorithm. We furthermore suggest that this collection should comprise all simple (few-body) operators in the theory, which echoes the applications of Nielsen complexity to dynamical evolution. The resulting construction, unlike the conventional Krylov complexity, reliably distinguishes integrable and chaotic Hamiltonians without any need for fine-tuning. Show Chinese abstract

Abstract: Krylov复杂度是衡量量子算符在动力学演化过程中在所有可能算符空间中扩展速度的一个有吸引力的量度。 人们预期其晚期平台值可以区分可积和混沌的动力学，但其区分能力取决于初始种子的选择，这非常脆弱。我们提议不将其应用于单一算符，而是像块兰索斯算法那样同时应用于一组初始种子。 此外，我们认为这一组种子应该包含理论中的所有简单（少体）算符，这与Nielsen复杂度在动力学演化中的应用相呼应。 所得到的构造，与传统的Krylov复杂度不同，无需任何精细调整就能可靠地区分可积和混沌哈密顿量。