Condensates, crystals, and renormalons in the Gross-Neveu model at finite density

TL;DR

This paper investigates the finite-density Gross-Neveu model, revealing new scales, inhomogeneous condensate phases, and insights into nonperturbative effects like renormalons using multiple theoretical techniques.

Contribution

It introduces the emergence of two dynamical scales and inhomogeneous condensate phases in the finite-density Gross-Neveu model, combining various methods to analyze nonperturbative phenomena.

Findings

Discovery of two scales, Λ_n and Λ_c, governing fermion mass gaps.

Identification of inhomogeneous condensate phases at high chemical potential.

Resolution of fractional-power renormalon puzzles and prediction of new ones.

Abstract

We study the $O(2N)$ symmetric Gross-Neveu model at finite density in the presence of a $U(1)$ chemical potential $h$ for a generic number $a \leq N-2$ of fermion fields. By combining perturbative quantum field theory, semiclassical large $N$, and Bethe ansatz techniques, we show that at finite $N$ two new dynamically generated scales $\Lambda_\mathrm{n}$ and $\Lambda_\mathrm{c}$ appear in the theory, governing the mass gap of neutral and charged fermions, respectively. Above a certain threshold value for $h$, $a$-fermion bound states condense and form an inhomogeneous configuration, which at infinite $N$ is a crystal spontaneously breaking translations. At large $h$, this crystal has mean $\Lambda_\mathrm{n}$ and spatial oscillations of amplitude $2\Lambda_\mathrm{c}$. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.