Peierls instability for systems with several Fermi surfaces: An example from the chiral Gross-Neveu model

As is well known, the chiral Gross-Neveu model at finite density can be solved semiclassically with the help of the chiral spiral mean field. The fermion spectrum has a single gap right at the Fermi energy, a reflection of the Peierls instability. Here, we divide the N fermion flavors into two subsets to which we attribute two different densities. The Hartree-Fock ground state of such a system can again be found analytically, using as mean field the “twisted kink crystal” of Basar and Dunne. Its spectrum displays two gaps with lower edges coinciding with the two Fermi energies. This solution is favored over the homogeneous one, providing us with an explicit example of a multiple Peierls instability.