Geometric-phase control of Krylov complexity in adiabatic dynamics
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.
Related
BibTeX
@misc{zheng2026geometricphase,
title = {{Geometric-phase control of Krylov complexity in adiabatic dynamics}},
author = {Han-Qi Zheng and Peng-Zhang He and Lei-Hua Liu and Hai-Qing Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.14325},
eprint = {2608.14325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.14325},
}
RIS
TY - UNPB
TI - Geometric-phase control of Krylov complexity in adiabatic dynamics
AU - Han-Qi Zheng
AU - Peng-Zhang He
AU - Lei-Hua Liu
AU - Hai-Qing Zhang
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.14325
UR - https://arxiv.org/abs/2608.14325
AB - 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.
ER -