A Twisted Kink Crystal in the Chiral Gross-Neveu model

TL;DR

This paper analyzes a crystalline chiral condensate in the massless chiral Gross-Neveu model, deriving exact solutions and spectral properties, and providing a comprehensive understanding of inhomogeneous condensates.

Contribution

It introduces a self-consistent crystalline condensate solution reducing the gap equation to a solvable nonlinear Schrödinger equation, unifying known solutions and deriving spectral properties.

Findings

Exact crystalline solutions to the gap equation.

Spectral properties of the inhomogeneous condensate derived.

All-orders Ginzburg-Landau expansion provided.

Abstract

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.