  Condensed matter physics of gauge theories coupled to fermions can exhibit a
rich phase structure, but are nevertheless very difficult to study in Monte
Carlo simulations when they are afflicted by a sign problem. As an alternate
approach, we use tensor network methods to explore the finite density physics
of Abelian gauge theories without dynamical matter. As a concrete example, we
consider the U(1) gauge invariant quantum link ladder with spin-1/2 gauge
fields in an external electric field which cause the winding electric fluxes to
condense in the ground state. We demonstrate how the electric flux tubes
arrange themselves in the bulk giving rise to crystalline patterns, whose
period can be controlled by tuning the external field. We propose observables
to detect the transitions in ground state properties not only in numerical
experiments, but also in future cold-atom realizations. A systematic procedure
for reaching the thermodynamic limit, as well as extending the studies from
ladders to extended geometries is outlined.
