  Gauge theories are of paramount importance in our understanding of
fundamental constituents of matter and their interactions. However, the
complete characterization of their phase diagrams and the full understanding of
non-perturbative effects are still debated, especially at finite charge
density, mostly due to the sign-problem affecting Monte Carlo numerical
simulations. Here, we report the Tensor Network simulation of a three
dimensional lattice gauge theory in the Hamiltonian formulation including
dynamical matter: Using this sign-problem-free method, we simulate the ground
states of a compact Quantum Electrodynamics at zero and finite charge
densities, and address fundamental questions such as the characterization of
collective phases of the model, the presence of a confining phase at large
gauge coupling, and the study of charge-screening effects.
