量子绝热动力学中的Krylov复杂度与Berry相位
Geometric-phase control of Krylov complexity in adiabatic dynamics
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中文总结 AI 辅助
本文在缓慢演化自旋系统的瞬时本征态基下，研究了量子绝热动力学中Krylov复杂度与Berry相位的关联，发现初始Krylov基为叠加态时Krylov复杂度非零，单量子比特系统中其振荡频率与外场强度和Berry相位相关。
中文摘要 AI 辅助
本文在缓慢演化自旋系统的瞬时本征态基下，研究了绝热动力学中Krylov复杂度与Berry相位的关联。若初始Krylov基是哈密顿量的瞬时本征态，绝热动力学将使Krylov复杂度消失；但研究表明，若初始Krylov基是叠加态而非本征态，Krylov复杂度将非零。Krylov复杂度的时间演化取决于控制参数，表现为周期性或准周期性。特别地，对于参数恒定的单量子比特系统，Krylov复杂度将随时间简谐振荡，其频率与外场强度和几何Berry相位的组合相关。
英文摘要
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.
发表机构
- Beihang University（北京航空航天大学）
- China West Normal University（西华师范大学）
- Jishou University（吉首大学）
- Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究院）
机构由 AI 辅助整理，请以论文原文为准。
