First-order phase boundaries of the massive ( 1+1 )-dimensional Nambu–Jona-Lasinio model with isospin

Abstract

The massive two-dimensional Nambu-Jona-Lasinio model with isospin (isoNJL) is reconsidered in the large Nc limit. We continue the exploration of its phase diagram by constructing missing first-order phase boundaries. At zero temperature, a phase boundary in the plane of baryon and isospin chemical potentials separates the vacuum from a crystal phase. We derive it from the baryon spectrum of the isoNJL model which, in turn, is obtained via a numerical Hartree-Fock (HF) calculation. At finite temperature, a first-order phase boundary sheet is found using a thermal HF calculation. It interpolates smoothly between the zero temperature phase boundary and the perturbative sheet. The calculations remain tractable owing to the assumption that the charged pion condensate vanishes. In that case, most of the calculations can be done with methods developed in the past for solving the massive one-flavor NJL model. * michael.thies@gravity.fau.de

Ordered Patterns of (3+1)-Dimensional Hadronic Gauged Solitons in the Low-Energy Limit of Quantum Chromodynamics at a Finite Baryon Density, Their Magnetic Fields and Novel BPS Bounds

“…In particular, the existence of nonhomogeneous Baryonic condensates is a genuine result of the fact that a finite amount of topological charge is "forced to live" within a finite spatial region (otherwise, in free space, such condensates would not form). In (1+1)-dimensional models (where the "solitons" are kinks, such as in the Gross-Neveu model and its variants; see, for instance, [29][30][31][32][33][34][35][36][37][38]), it is clear by now that there is a finite region in the phase diagram (which appears at a finite density) where kink crystals (namely, ordered arrays of kinks) dominate. Similar results further supporting the appearance of non-homogeneous condensates have been obtained in higher-dimensional models (under the assumption that the main fields only depend on one spatial coordinate, see [16][17][18][19][20] and the references therein).…”

“…Both types of results strongly suggest that similar phenomena should appear at the low-energy limit of QCD in (3+1) dimensions as well. The models analyzed in [29][30][31][32][33][34][35][36][37][38] are considered very good toy models of QCD at a finite Baryon density. In such models, the formation of ordered patterns of solitons is well understood theoretically (due to integrability).…”