The phase diagram of QCD is of fundamental interest for high energy physics, cosmology and astrophysics, but at the present moment ab-initio calculations in the lattice QCD formalism at finite density are impossible. However, in the regions of high temperature and small density or of high density and small temperature theories with SU(2) and SU(3) gauge groups with the presence of fundamental fermions are expected to have similar properties. SU(2) theory in lattice formulation does not possess a sign problem, which makes computations at finite density possible. I will present results for the phase structure of lattice SU(2) QCD with two flavors of quarks at finite quark density and zero temperature. Interaction properties of quarks, real-time inter-quark potential and the confinement/deconfinement transition will be examined. Our results indicate that in very dense matter the quark-gluon plasma is in essence a weakly interacting gas of quarks and gluons without a magnetic screening mass in the system, sharply different from a QGP at large temperature. The talk is based on papers arXiv:1808.06466, 1711.01869, 1605.04090, and recent results.