发表机构
Georg-August-Universität Göttingen; University of Southern California（哥廷根大学; 南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出Krylov边缘谱学，利用边界算子动力学检测一维对称保护拓扑相，无需精确对角化，并在簇链中揭示局域化转变。\n
AI 中文摘要
我们引入了 Krylov 边缘谱学，这是一种多体算子空间协议，用于从局部边界动力学中检测和分类一维对称保护拓扑相。一个厄米边界算子生成一个半无限 Krylov 跳跃链，其边界权重满足精确的零频归一化判据。开周期、边界-体以及对称保持的边界微扰测试可识别受保护的边界记忆，而有限深度泄漏残差则用于确认显式重构的算子是否已接近零频。分类过程在固定电荷扇区内，对对称分辨的边界算子最小化归一化对易子。对于玻色型 Z_N × Z_N 相，恢复的端点电荷给出上同调标签。该方法既不需要多体精确对角化、显式的基态波函数或纠缠谱，也不需要猜测的修饰边缘或弦算子。对于有限程哈密顿量，局域性在深度极限之前，于固定 Krylov 深度下组织了热力学极限。我们在簇、时钟、Haldane 以及平凡自旋-1 链中演示了该协议。在可精确求解的簇链中，有能隙拓扑相与平凡相之间的转变表现为 Krylov 链上 Krylov 边缘模式的局域化-去局域化转变。该转变恰好发生在体能隙闭合处，其局域化长度指数与 Ising 关联长度指数一致。通过算子 Krylov 动力学，我们的工作将局部边界演化转变为多体拓扑的直接谱学手段。
英文摘要
We introduce $Krylov$ $edge$ $spectroscopy$, a many-body operator-space protocol for detecting and classifying one-dimensional symmetry-protected topological phases from local boundary dynamics. A Hermitian boundary operator generates a semi-infinite Krylov hopping chain whose boundary weight obeys an exact zero-frequency normalizability criterion. Open-periodic, boundary-bulk, and symmetry-preserving boundary-perturbation tests identify protected boundary memory, while a finite-depth leakage residual certifies when an explicitly reconstructed operator is already near zero frequency. Classification minimizes the normalized commutator over symmetry-resolved boundary operators in fixed charge sectors. For bosonic $\mathbb{Z}_N \times \mathbb{Z}_N$ phases, the recovered endpoint charge gives the cohomology label. The method requires no explicit ground-state wavefunction, entanglement spectrum, or guessed dressed edge or string operator. For finite-range Hamiltonians, locality eliminates full-system exact diagonalization and guarantees thermodynamic-limit convergence at fixed Krylov depth. We demonstrate the protocol in cluster, clock, Haldane, and trivial spin-1 chains. In the exactly solvable cluster chain, the transition between the gapped topological and trivial phases manifests as a localization-delocalization transition of the Krylov edge mode on the Krylov chain. This transition occurs precisely at the bulk gap closing, and its localization-length exponent coincides with the Ising correlation-length exponent. Through operator Krylov dynamics, our work turns local boundary evolution into a direct spectroscopy of many-body topology.
Comments5+29 pages, 2 figures, 2 tables
