Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems

TL;DR

This paper presents a new exact self-consistent crystalline condensate solution in 1+1 dimensional models, linking quantum field theory and superconductivity, with implications for phase diagrams.

Contribution

It introduces a novel exact crystalline condensate solution applicable to the chiral Gross-Neveu and Bogoliubov-de Gennes systems, unifying different theoretical frameworks.

Findings

Derived a new exact crystalline condensate in the chiral Gross-Neveu model.

Provided a corresponding solution for the Bogoliubov-de Gennes equations.

Reduced the gap equation to a solvable nonlinear form, impacting phase diagram analysis.

Abstract

We derive a new exact self-consistent crystalline condensate in the 1+1 dimensional chiral Gross-Neveu model. This also yields a new exact crystalline solution for the one dimensional Bogoliubov-de Gennes equations and the Eilenberger equation of semiclassical superconductivity. We show that the functional gap equation can be reduced to a solvable nonlinear equation, and discuss implications for the temperature-chemical potential phase diagram.