Analytical solution of the Gross-Neveu model at finite density

TL;DR

This paper provides an analytical solution for the Gross-Neveu model at finite density, revealing a crystalline ground state and connecting it to elliptic functions and non-relativistic Hamiltonians, with implications for relativistic superconductors.

Contribution

It presents the first analytical solution to the finite-density Gross-Neveu model using elliptic functions, building on recent numerical findings.

Findings

Ground state is a crystal structure.

Scalar potential linked to elliptic functions.

Model serves as a toy for relativistic superconductor phases.

Abstract

Recent numerical calculations have shown that the ground state of the Gross-Neveu model at finite density is a crystal. Guided by these results, we can now present the analytical solution to this problem in terms of elliptic functions. The scalar potential is the superpotential of the non-relativistic Lame Hamiltonian. This model can also serve as analytically solvable toy model for a relativistic superconductor in the Larkin-Ovchinnikov-Fulde-Ferrell phase.