Superdiffusion and the chaotic-integrable crossover in Heisenberg spin-chains

Motivated by lessons drawn from scrambling in random circuits, we implement a Heiseberg operator evolution algorithm that artificially dissipates non-local operators—we call the method dissipation-assisted operator evolution (DAOE). The algorithm can efficiently evolve hydrodynamical observables to late times using a matrix product state representation, and has already been used to accurately predict spin/energy diffusion constants in non-integrable spin-chain models. In this work we use DAOE to obtain well-converged predictions for the super-diffusion exponent and super-diffusion constant in the isotropic XXZ chain and discuss the crossover between integrable and chaotic dynamics in experimentally accessible quantum magnets.