Generalized Beth-Uhlenbeck Approach to the 2+1D Gross-Neveu Model

TL;DR

This paper develops a generalized Beth-Uhlenbeck approach to analyze the thermodynamics of the (2+1)D Gross-Neveu model, highlighting the significant role of fluctuations and bound states in entropy and crossover phenomena.

Contribution

It introduces a self-consistent, generalized Beth-Uhlenbeck framework that accounts for fluctuation back-reaction and modifies low-energy contributions in the 2+1D Gross-Neveu model.

Findings

Fluctuations contribute significantly to entropy, comparable to mean field.

The generalized approach suppresses low-energy contributions while preserving bound states.

Results show a sharper crossover consistent with Mott-transition physics.

Abstract

We study the thermodynamics of the (2+1) dimensional Gross-Neveu model inspired from graphene. We focus on the entropy density of the Gaussian fluctuation beyond the mean field. The full in-medium, momentum-dependent evaluation reveals that the fluctuations give a substantial contribution, even comparable to that of the mean field. We argue that the back-reaction from the fluctuations to the mean field should be included, which reduces the contribution mainly coming from the Landau-damping region. To treat this self-consistently, we use the generalized version of the Beth-Uhlenbeck approach for the entropy density. Compared with the standard Beth-Uhlenbeck formulation, the generalized version suppresses the low-energy contributions while preserving the bound-state effects. The fractional entropy carried by bound excitons and free fermions reveals a sharper crossover of the degrees of freedom in the generalized version, which is consistent with Mott-transition physics in two-dimensional materials.