A Twisted Kink Crystal in the Chiral Gross-Neveu model

Details A Twisted Kink Crystal in the Chiral Gross-Neveu model A Twisted Kink Crystal in the Chiral Gross-Neveu model

2008-06-16

arxiv.org/abs/0806.2659v2

Phys.Rev.D78:065022,2008

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 13 figs; v2: new appendix on Eilenberger eq and refs; version in PRD

Scientific paper

10.1103/PhysRevD.78.065022

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. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order-by-order.

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