Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model

TL;DR

This paper derives a Beth-Uhlenbeck equation for Gaussian fluctuations in a generalized 2+1D Gross-Neveu model inspired by Graphene, revealing new insights into phase shifts, bound states, and fluctuation pressure.

Contribution

It introduces a numerical approach to include momentum dependence in phase shifts, advancing beyond mean field approximation in this model.

Findings

Resurrection of pseudoscalar bound states at high momentum

Significant contribution of Landau modes to fluctuation pressure

Momentum dependence alters phase shift behavior compared to previous models

Abstract

We study a generalized version of the Gross-Neveu model in 2+1 dimensions. The model is inspired from Graphene, which shows a linear dispersion relation near the Dirac points. The phase structure and the thermodynamic properties in the mean field approximation have been studied before. Here, we go beyond the mean field level by deriving a Beth-Uhlenbeck equation for Gaussian fluctuations formulated in phase shift solutions, which we explore numerically, for the first time including their momentum dependence. We discuss the excitonic mass, fluctuation pressure, and phase shifts. The inclusion of momentum dependence in the phase shift shows a significant difference from the Lorentz-boosted version of the phase shift previously used in the literature. We find resurrection of the pseudoscalar bound states at large momentum above Mott temperature and show that the presence of Landau modes significantly contributes to the fluctuation pressure.