Dominik Vuina: Non-equilibrium dynamics in quantum systems

Quantum systems, when pushed out of equilibrium and allowed to relax, can exhibit intriguing phenomena. I will discuss the relaxation, or non-equilibrium dynamics, of a quantum system with constrained motion of its degrees of freedom. 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 experiments' ability to measure the properties of the entire sector. We show that additional controlled dephasing reliably mixes the system within a single Krylov sector, and that simple observables can differentiate these sectors. For example, in the strongly interacting XXZ chain with dephasing, the spin imbalance between even and odd sublattices distinguishes sectors. For appropriate choices of initial states, the imbalance begins positive, decays to a negative minimum value at intermediate times, and eventually returns to zero. The minimum reflects the average imbalance of the Krylov sector associated to the initial state. We compute the size of the minimum analytically in the limit of strong interactions, and validate our results with simulations at experimentally relevant interaction strengths. I will also briefly discuss other works that form a part of my thesis."