Thermodynamics of a generalized graphene-motivated (2+1)-dimensional Gross-Neveu model beyond mean field within the Beth-Uhlenbeck approach

Abstract

We investigate the thermodynamics at finite density of a generalized $(2+1)$-dimensional Gross-Neveu model of $N$ fermion species with various types of four-fermion interactions. The motivation for considering such a generalized schematic model arises from taking the Fierz-transformation of an effective Coulomb current-current interaction and certain symmetry breaking interaction terms, as considered for graphene-type models in Ref. [16]. We then apply path-integral bosonization techniques, based on the large $N$ limit, to derive the thermodynamic potential. This includes the leading order mean-field (saddle point) contribution as well as the next-order contribution of Gaussian fluctuations of exciton fields. The main focus of the paper is then the investigation of the thermodynamic properties of the resulting fermion-exciton plasma. In particular, we derive an extended Beth-Uhlenbeck form of the thermodynamic potential, discuss the Levinson theorem and the decomposition of the phase of the exciton correlation into a resonant and scattering part.

31 pages, 2 figures, version accepted for publication in Prog. Theor. Exp. Phys

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• Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Casimir effect for fermion condensate in conical rings
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model
• Generalized Beth-Uhlenbeck Approach to the 2+1D Gross-Neveu Model