  The mechanism underlying charge transport in strongly correlated quantum
systems, such as doped antiferromagnetic Mott insulators, remains poorly
understood. Here we study the expansion dynamics of an initially localized hole
inside a two-dimensional (2D) Ising antiferromagnet at variable temperature.
Using a combination of classical Monte Carlo and a truncated basis method, we
reveal two dynamically distinct regimes: A spin-charge confined region below a
critical temperature $T^*$, characterized by slow spreading, and a spin-charge
deconfined region above $T^*$, characterized by an unbounded diffusive
expansion. The deconfinement temperature $T^*\approx 0.65 J_z$ we find is
around the N\'eel temperature $T_{\rm N} = 0.567 J_z$ of the Ising background
in 2D, but we expect $T^* < T_{\rm N}$ in higher dimensions. In both regimes we
find that the mobile hole does not thermalize with the Ising spin background on
the considered time scales, indicating weak effective coupling of spin- and
charge degrees of freedom. Our results can be qualitatively understood by an
effective parton model, and can be tested experimentally in state-of-the-art
quantum gas microscopes.
