A tracer diffusion interpretation of anomalous transport in constrained quantum matter

In recent works a zoo of constrained quantum many-body systems with anomalous transport properties has been identified. A crucial challenge now is to distill potential underlying unifying principles giving rise to such anomalous transport. Here, we will show that for various constrained quantum systems the concept of tracer diffusion, that is diffusion of tagged particles with infinite-repulsive interactions, provides intriguing insights into their anomalous transport properties. A central ingredient for our interpretation is to identify conserved charge patterns in constrained quantum systems through an appropriate change of variables. We will apply this concept both to non-integrable random unitary circuit models as well as to integrable systems, including the t-Jz Hamiltonian in the weak Jz limit and the folded Heisenberg model (the Heisenberg model with infinitely strong easy-axis anisotropy). For these systems, tracer diffusion even allows us to calculate the exact values and the parameter dependence of microscopic diffusion constants.