  We explore the ground-state physics of two-dimensional spin-$1/2$ $U(1)$
quantum link models, one of the simplest non-trivial lattice gauge theories
with fermionic matter within experimental reach for quantum simulations.
Whereas in the large mass limit we observe Ne\'el-like vortex-antivortex and
striped crystalline phases, for small masses there is a transition from the
striped phases into a disordered phase whose properties resemble those at the
Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized
on ladders by boundary Haldane-like properties, such as vanishing parity and
finite string ordering. Moreover, from studies of the string tension between
gauge charges, we find that whereas the stripe phases are confined, the novel
disordered phase present clear indications of being deconfined. Our results
open exciting perspectives of studying highly non-trivial physics in quantum
simulators, such as spin-liquid behavior and confinement-deconfinement
transitions, without the need of explicitly engineering plaquette terms.
