Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 16: Many-body Systems: Equilibration, Chaos, and Localization (joint session DY/TT)

DY 16.2: Talk

Tuesday, March 18, 2025, 14:15–14:30, H37

Escaping the Krylov space during reorthogonalization — •Max Pieper, Jannis Eckseler, and Jürgen Schnack — Universität Bielefeld

Krylov complexity [1] is often used as a measure of complexity in quantum many-body-systems. During its calculation, the Lanzcos algorithm is used to construct an operator basis. Due to the poor orthogonality of the resulting basis reorthogonalization is often employed [2]. We investigate how using reorthogonalization causes the Lanczos algorithm to accumulate non-Krylov basis elements. We suspect this to negatively affect the Krylov algorithm.

[1] D. E. Parker et al. Phys. Rev. X 9, 041017 (2019)

[2] E. Rabinovici et al. JHEP 06, 062 (2021)

Keywords: Krylov complexity; Krylov space; Lanzcos algorithm; Reorthogonalization