Particle formation and ordering in strongly correlated fermionic systems: Solving a model of quantum chromodynamics

In this paper we study a (1 + 1)-dimensional version of the famous Nambu-Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, mu, is zero, we describe the formation of fermion three-quark (nucleons and Delta baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at mu = 0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, 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). The QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).