标题： 块对角算子的增长和对称性分辨的Krylov复杂度 显示英文标题

标题： Growth of block diagonal operators and symmetry-resolved Krylov complexity

摘要： 这项工作探讨了不变算符的增长如何受到其底层对称结构的影响。 为此，我们引入了对称性分辨的Krylov复杂度，它捕捉了在给定对称性下，一个算符可以分解成的每个块的时间演化。 我们发现，在早期时间，整个算符的复杂度等于对称性分辨贡献的平均值。 然而，在较晚的时间，不同电荷子空间之间的相互作用变得更加复杂。 一般来说，对称性分辨的Krylov复杂度取决于电荷子空间，尽管在某些情况下这种依赖性消失，导致Krylov复杂度的均分形式。 我们的分析为在研究Krylov空间复杂度中更广泛地应用对称结构奠定了基础，这对多体量子系统中的热化和普适性具有重要意义。 显示英文摘要

摘要： This work addresses how the growth of invariant operators is influenced by their underlying symmetry structure. For this purpose, we introduce the symmetry-resolved Krylov complexity, which captures the time evolution of each block into which an operator, invariant under a given symmetry, can be decomposed. We find that, at early times, the complexity of the full operator is equal to the average of the symmetry-resolved contributions. At later times, however, the interplay among different charge sectors becomes more intricate. In general, the symmetry-resolved Krylov complexity depends on the charge sector, although in some cases this dependence disappears, leading to a form of Krylov complexity equipartition. Our analysis lays the groundwork for a broader application of symmetry structures in the study of Krylov space complexities with implications for thermalization and universality in many-body quantum systems.