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arXiv · 2608.14325

Geometric-phase control of Krylov complexity in adiabatic dynamics

Han-Qi Zheng·Peng-Zhang He·Lei-Hua Liu·Hai-Qing Zhang
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Abstract

We show that geometric phases accumulated during adiabatic evolution can be converted into observable interference in Krylov space, leading to a geometric-phase-dependent Krylov oscillation. Adiabatic dynamics force Krylov complexity to vanish if the initial Krylov basis is an instantaneous eigenstate of the Hamiltonian; Nevertheless, we demonstrate that the Krylov complexity will be non-vanishing if the initial Krylov basis is a superposition state rather than an eigenstate. Consequently, Krylov complexity is found to depend on the difference of dynamical phases in the Krylov space, which is deeply related to the Berry connections in the original Hilbert space. In particular, for a single qubit system with constant Lanczos coefficients, Krylov complexity oscillates harmonically at a frequency given by the strength of the external field and the geometric Berry phase. Therefore, our work may provide a novel avenue to probe the geometric phase from the Krylov complexity.

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Han-Qi Zheng, Peng-Zhang He, Lei-Hua Liu, Hai-Qing Zhang. 2026-08-14. Geometric-phase control of Krylov complexity in adiabatic dynamics. https://arxiv.org/abs/2608.14325

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