Quantum Walk in Degenerate Spin Environments

We study the propagation of a hole in degenerate (paramagnetic) spin environments. This canonical problem has important connections to a number of physical systems, and is perfectly suited for experimental realization with ultracold atoms in an optical lattice. At the short-to-intermediate time scale that we can access using a stochastic-series-type numeric scheme, the propagation turns out to be distinctly nondiffusive with the probability distribution featuring minima in both space and time due to quantum interference, yet the motion is not ballistic, except at the beginning. We discuss possible scenarios for long-term evolution that could be explored with an unprecedented degree of detail in experiments with single-atom resolved imaging.