Quantum Walk in Degenerate Spin Environments

TL;DR

This paper investigates how a hole propagates in degenerate spin environments, revealing non-diffusive quantum interference effects and discussing potential long-term behaviors observable in ultra-cold atom experiments.

Contribution

It provides the first detailed numerical analysis of hole dynamics in paramagnetic spin environments, highlighting non-diffusive quantum interference effects.

Findings

Propagation is non-diffusive with minima in probability distribution due to quantum interference

Motion is not ballistic except at initial times

Potential for detailed experimental exploration of long-term evolution

Abstract

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.