We study generic properties of strongly interacting matter at finite density as relevant to heavy-ion collisions at moderate beam energies or the physics of neutron stars and their mergers.
Because of the fermion-sign problem in lattice QCD, here we simulate QCD-like theories without this problem at finite density.
These theories (two-color QCD, G2-QCD, ... ) typically contain bosonic baryons, for example diquarks.
It is therefore important to understand the effects of such bosonic matter and disentangle them from fermionic baryons where they exist to draw conclusions for QCD.
Simulations of these theories, for instance G2-QCD, reveal an interesting and rich phase diagram at zero temperature.
Many open questions arise, partly due to the lack of high precision or large volume/continuum data.
This is the reason why we study two-dimensional QCD-like theories. In this contribution we shall discuss differences between QCD-like theories at baryon chemical and isospin chemical potential.
Furthermore we present simulation results on the phase diagram and spectroscopy at finite density for G2- and two-color-QCD and compare it to free lattice fermions.