Emergent integrability in Heisenberg spin models with disordered couplings
Disordered quantum many-body systems can show striking phenomena such as slow relaxation or many-body localization. Quantum simulation experiments have proven a useful tool for understanding the dynamics of such non-integrable systems beyond system sizes accessible to numerical methods. In this talk, I present recent results from theory and experiment concerning the dynamics of spatially disordered Heisenberg-type models with power-law interactions. Concretely, we used a cold gas of Rydberg atoms to realize Ising, XXZ and XX models and found the relaxation dynamics of the global magnetization to be universal with respect to a typical timescale. The origin of this universal behavior lies within the disordered couplings which lead to the formation of strongly interacting pairs of spins that constitute quasi-conserved quantities for long periods of time. Higher order perturbation theory reveals a strong renormalization group flow towards an effective Ising model of clusters of spins.