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Dynamical signatures of thermal spin-charge deconfinement in the doped Ising model

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 Néel 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.