Condensates, Crystals, and Renormalons in the Gross-Neveu Model at Finite Density

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≤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 Λn and Λc 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 Λn and spatial oscillations of amplitude Λc. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.