  The absence of thermalization in certain isolated many-body systems is of
great fundamental interest. Many-body localization (MBL) is a widely studied
mechanism for thermalization to fail in strongly disordered quantum systems,
but it is still not understood precisely how the range of interactions affects
the dynamical behavior and the existence of MBL, especially in dimensions
$D>1$. By investigating nonequilibrium dynamics in strongly disordered $D=2$
electron systems with power-law interactions $\propto 1/r^{\alpha}$ and poor
coupling to a thermal bath, here we observe MBL-like, prethermal dynamics for
$\alpha=3$. In contrast, for $\alpha=1$, the system thermalizes, although the
dynamics is glassy. Our results provide important insights for theory,
especially since we obtained them on systems that are much closer to the
thermodynamic limit than synthetic quantum systems employed in previous studies
of MBL. Thus, our work is a key step towards further studies of ergodicity
breaking and quantum entanglement in real materials.
