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 ultra-cold atoms in an optical lattice. At the short-to-intermediate timescale that we can access using a stochastic-series-type numeric scheme, the propagation turns out to be distinctly non-diffusive with the proba- bility 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.
@article{arxiv.1602.05366,
title = {Quantum Walk in Degenerate Spin Environments},
author = {Johan Carlström and Nikolay Prokof'ev and Boris Svistunov},
journal= {arXiv preprint arXiv:1602.05366},
year = {2016}
}