Critical flavour number of the Thirring model in three dimensions

TL;DR

This paper investigates the critical number of fermion flavors in the three-dimensional Thirring model, using SLAC fermions to better understand the chiral phase transition and address limitations of previous lattice studies.

Contribution

It introduces a new lattice simulation approach with SLAC fermions to accurately study the chiral symmetry breaking in the Thirring model.

Findings

Initial simulation results obtained with SLAC fermions.

No reliable estimate of the critical flavor number yet.

Highlights the importance of chiral symmetry preservation in lattice studies.

Abstract

The Thirring model is a four fermion theory with vector interaction. We study it in three dimensions, where it is closely related to QED and other models used to describe properties of graphene. In addition it is a good toy model to study chiral symmetry breaking, since a phase with broken chiral symmetry is present for the model with one fermion flavour. On the other hand, there is no such phase in the limit of infinitely many fermion flavours. Thus, a transition at some critical flavour number Nfc is expected, where the broken phase vanishes. The model was already studied with different methods, including Schwinger-Dyson, functional renormalization group and lattice approaches. Most studies agree that there is indeed a phase transition from a chirally symmetric phase to a spontaneously broken phase for a small number of fermion flavours. But there is no agreement on the critical flavour number and further details of the critical behaviour. Values of Nfc found in the literature usually range between 2 and 7. All earlier lattice studies were performed with staggered fermions, where it is questionable if the continuum limit of the lattice model has the same chiral symmetry as the continuum model. We present an approach for simulations of the Thirring model with SLAC fermions. With this choice, we can be sure to implement the full chiral symmetry of the continuum model. First results from simulations are shown but do not allow a reliable estimate of Nfc so far.