Extension of the Krylov-complexity–Berry-phase connection to the Aharonov–Bohm effect

Extend the established connection between Krylov complexity and geometric phase in adiabatic spin dynamics to other models exhibiting geometric phases, specifically including the Aharonov–Bohm effect.

Background

The paper derives an explicit relation between the oscillation frequency of Krylov complexity and the Berry phase for a slowly driven single-qubit system. For a closed rotation of the external field, the frequency is given by $\nu=h-2\gamma_B/T$, linking the external-field strength and the Berry phase to Krylov-complexity dynamics.

The authors suggest that this connection may apply beyond Berry-phase spin systems to other physical models with geometric phases, naming the Aharonov–Bohm effect as a specific example. No derivation or proof of such an extension is provided in the paper, and the authors explicitly leave it for future work.