Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

TL;DR

This paper investigates the Fermi surface phenomena in the (2+1)d Gross-Neveu model with a chemical potential, combining analytical calculations and lattice simulations to explore in-medium effects and collective excitations.

Contribution

It provides the first combined analytical and numerical study of Fermi surface effects in the (2+1)d four-Fermi model at finite density, including in-medium meson properties and zero sound evidence.

Findings

Confirmation of Fermi surface formation at high chemical potential

Observation of in-medium scalar propagator modifications

Evidence for zero sound-like excitations in the vector channel

Abstract

We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu using both analytical and numerical methods. For mu greater than a critical value the model is chirally symmetric and has a Fermi surface with Fermi momentum ~mu. We have calculated the particle interaction in medium due to scalar meson exchange to leading order in 1/N, where N is the number of flavors, in the hard dense loop approach. The result has been used to calculate the relation between mu and the Fermi momentum and velocity in the resulting Fermi liquid to O(1/N). Simulation results from a 32^2x48 lattice for fermion and meson dispersion relations and meson wavefunctions are then presented, showing qualitative and in some cases quantitative agreement with analytic predictions. In particular, the simulations show clear evidence for the in-medium modification of the scalar propagator, oscillatory behaviour in the wavefunction consistent with a sharp Fermi surface, and tentative evidence for a massless pole in the vector meson channel resembling zero sound.