Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model

TL;DR

This study applies the Maximum Entropy Method to analyze spectral functions in a (2+1)d four-fermion lattice model, revealing insights into mesonic states, phase behavior, and non-perturbative effects.

Contribution

It demonstrates the effectiveness of the Maximum Entropy Method in extracting spectral functions and characterizes mesonic spectra and resonances in both broken and symmetric phases of the model.

Findings

Confirmed Goldstone nature of the pion.

Estimated meson binding energy.

Observed resonance with non-zero width in symmetric phase.

Abstract

We investigate spectral functions extracted using the Maximum Entropy Method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma and massive pseudoscalar meson; our results confirm the Goldstone nature of the pi and permit an estimate of the meson binding energy. We have, however, seen no signal of sigma -> pi pi decay as the chiral limit is approached. In the symmetric phase we observe a resonance of non-zero width in qualitative agreement with analytic expectations; in addition the ultra-violet behaviour of the spectral functions is consistent with the large non-perturbative anomalous dimension for fermion composite operators expected in this model.