Probing hydrodynamic crossovers with dissipation-assisted operator evolution

Emergent hydrodynamic behavior that arises in many-body dynamics of a quantum system at long times is best understood at extreme parameter regimes such as at high or low temperatures where the theory and numerics is well controlled. However, intermediate regimes where most physical systems lie is less understood. Here, we develop a novel technique to probe hydrodynamic crossovers across wide range of parameter regimes through a modified version of dissipation-assisted operator evolution (DAOE), a method which aims to reduce operator entanglement by suppressing components that negligibly contribute to hydrodynamic correlations during time evolution. We specifically test our method on a system with U(1) conserved charge and study such a crossover by computing diffusion constant for a wide range of filling fractions.