Finite-temperature screening of U(1) fractons

We investigate the finite-temperature screening behavior of three-dimensional $U(1)$ spin-liquid phases with fracton excitations. Several features are shared with the conventional $U(1)$ spin liquid. The system can exhibit spin-liquid physics over macroscopic length scales at low temperatures, but screening effects eventually lead to a smooth finite-temperature crossover to a trivial phase at sufficiently large distances. However, unlike more conventional $U(1)$ spin liquids, we find that complete low-temperature screening of fractons requires not only very large distances, but also very long time scales. At the longest time scales, a charged disturbance (fracton) will acquire a screening cloud of other fractons, resulting in only short-range correlations in the system. At intermediate time scales, on the other hand, a fracton can only be partially screened by a cloud of mobile excitations, leaving weak power-law correlations in the system. Such residual power-law correlations may be a useful diagnostic in an experimental search for $U(1)$ fracton phases.