D. Vuina: Probing Hilbert space fragmentation using controlled dephasing

Dynamical constraints in many-body quantum systems can lead to Hilbert space fragmentation, wherein the system’s evolution is restricted to small subspaces of Hilbert space called Krylov sectors. However, unitary dynamics within individual sectors may also be slow or non-ergodic, which limits the ability of experiments to measure properties of the entire sector. We show that additional controlled dephasing reliably mixes the system within a single Krylov sector, and that simple observables differentiate Krylov sectors. In particular, in the strongly interacting XXZ chain with dephasing, the spin imbalance between even and odd sublattices differentiates sectors. A striking signature is an imbalance overshoot: the positive imbalance of some initial states decays towards the negative average value in their Krylov sector, overshooting the maximally mixed expectation value of zero. On longer time scales, the imbalance relaxes to zero, so that the overshoot appears as an easily-identified minimum in the imbalance as a function of time. We compute the size of the overshoot analytically in the limit of strong interactions, and validate our results with simulations at experimentally relevant interaction strengths