Probing Krylov Dynamics in Driven Many-Body Systems

arXiv:2611.14611v1 Announce Type: new Abstract: Krylov complexity has become a central probe of operator growth, scrambling, and quantum chaos. Yet, a basic fact hinders its experimental study: laboratory quantum systems are routinely driven in time, whereas the Krylov construction assumes a fixed generator and breaks down once the Hamiltonian varies. Here, we solve the time-dependent many-body Krylov problem exactly and in closed form for scale- and rotation-invariant systems realized in current quantum-simulation and control platforms. We find exact relations that map the driven dynamics onto mutually orthogonal Krylov subspaces and yield a closed-form spread complexity, determined solely by the spectral properties of the initial Hamiltonian and the driving schedule.