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Condensates, Crystals, and Renormalons in the Gross-Neveu Model at Finite Density
Francesco Benini1, Ohad Mamroud1, Tomás Reis1
1INFN, Sezione di Trieste, SISSA, via Bonomea 265, 34136 Trieste, Italy and , via Valerio 2, 34127 Trieste, Italy.
None:
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.
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