Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin

The phase diagram of the two-dimensional Nambu--Jona-Lasinio model with isospin is explored in the large Nc limit with semiclassical methods. We consider finite temperature and include chemical potentials for all conserved charges. In the chiral limit, a full analytical solution is presented, expressed in terms of known results for the single-flavor Gross-Neveu and Nambu--Jona-Lasinio models. A novel crystalline structure appears and is shown explicitly to be thermodynamically more stable than the homogeneous phase at zero temperature. If we include a bare fermion mass, the problem reduces again to solved problems in one-flavor models provided that either the fermionic or the isospin chemical potentials vanish. In the general case, a stability analysis is used to construct the perturbative phase boundary between homogeneous and inhomogeneous phases. This is sufficient to get a good overview of the complete phase diagram. Missing non-perturbative phase boundaries requiring a full numerical Hartree-Fock calculation will be presented in future work.