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 Λ_{n} and Λ_{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 Λ_{n} and spatial oscillations of amplitude Λ_{c}. The two scales also control the nonperturbative corrections to the free energy, resolving a puzzle concerning fractional-power renormalons and predicting new ones.