Universal chaotic dynamics from Krylov space

Understand

Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state.

• We investigate the evolution of the maximally entangled state in the Krylov basis for both chaotic and non-chaotic systems.
• For this purpose, we derive an Ehrenfest theorem for the Krylov complexity, which reveals its close relation to the spectrum.
• Our findings suggest that neither the linear growth nor the saturation of Krylov complexity is necessarily associated with chaos.