A Twisted Kink Crystal in the Chiral Gross-Neveu model

Understand

We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model.

• We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schr\"odinger equation, which is exactly soluble.
• The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation.
• Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived.