Zero Lattice Sound

TL;DR

This paper investigates collective excitations in the 2+1D Gross-Neveu model at finite chemical potential, combining analytical quasiparticle analysis with lattice simulations to identify zero sound and phonon-like modes.

Contribution

It provides the first evidence of collective excitations in lattice simulations of the Gross-Neveu model at finite density, linking analytical and numerical approaches.

Findings

Identification of zero sound propagation for mu > mu_c

Observation of phonon-like excitations with linear dispersion

First lattice simulation evidence of collective modes in this context

Abstract

We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu, using both analytical and numerical methods. In particular, we study the self-consistent Boltzmann equation in the Fermi liquid framework using the quasiparticle interaction calculated to O(1/N_f), and find solutions for zero sound propagation for almost all mu > mu_c, the critical chemical potential for chiral symmetry restoration. Next we present results of a numerical lattice simulation, examining temporal correlation functions of mesons defined using a point-split interpolating operator, and finding evidence for phonon-like behaviour characterised by a linear dispersion relation in the long wavelength limit. We argue that our results provide the first evidence for a collective excitation in a lattice simulation.