  We study the interplay between magnetic frustration and itinerant electrons.
For example, how does the coupling to mobile charges modify the properties of a
spin liquid, and does the underlying frustration favor insulating or conducting
states? Supported by Monte Carlo simulations, our goal is in particular to
provide an analytical picture of the mechanisms involved. The models under
considerations exhibit Coulomb phases in two and three dimensions, where the
itinerant electrons are coupled to the localized spins via double exchange
interactions. Because of the Hund coupling, magnetic loops naturally emerge
from the Coulomb phase and serve as conducting channels for the mobile
electrons, leading to doping-dependent rearrangements of the loop ensemble in
order to minimize the electronic kinetic energy. At low electron density \rho,
the double exchange coupling mainly tends to segment the very long loops
winding around the system into smaller ones while it gradually lifts the
extensive degeneracy of the Coulomb phase with increasing \rho. For higher
doping, the results are strongly lattice dependent, displaying loop crystals
with a given loop length for some specific values of \rho, which can melt into
another loop crystal by varying \rho. Finally, we contrast this to the
qualitatively different behavior of analogous models on kagome or triangular
lattices.
