I present the results of a study of a (1 +1 )-dimensional version of the famous Nambu-Jona-Lasinio model of quantum chromodynamics both at zero and at finite baryon density. For zero chemical potential, we found the formation of fermionic (nucleons and Δ baryons) and bosonic (two-quark mesons, six-quark deuterons) excitations, and demonstrated the existence of a phase transition. For a finite baryon density the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Relevant publication: P. Azaria, R.M. Konik, Ph. Lecheminant, T. Pálmai, G. Takács and A.M. Tsvelik: Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics, Phys. Rev. D94 (2016) 045003, arXiv:1601.02979 [hep-th].