Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

Understand

Some time ago, Thies et al.

• showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase.
• Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lame potentials with a Darboux displacement depending on the bare mass.
• We study an unusual supersymmetry of such a second order Lame system, and show that the associated first order Bogoliubov-de Gennes Hamiltonian possesses the own nonlinear supersymmetry.