Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions

Abstract

The Thirring model is an interacting fermion theory with current-current interaction. The model in 1+2 dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials. Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors Nc exists, below which chiral symmetry can be broken spontaneously. Values for Nc found in the literature vary between 2 and 7. Recent lattice studies with chirally invariant SLAC fermions have indicated that chiral symmetry is unbroken for all integer flavor numbers [B. H. Wellegehausen, D. Schmidt, and A. Wipf, Phys. Rev. D 96, 094504 (2017); PRVDAQ2470-001010.1103/PhysRevD.96.094504D. Schmidt, Three-dimensional four-Fermi theories with exact chiral symmetry on the lattice, Ph.D. thesis, TPI, FS-University Jena, 2018, https://doi.org/10.22032/dbt.34148]. An independent simulation based on domain wall fermions seems to favor a critical flavor-number that satisfies 1 Nc and should answer the question of where to construct a continuum limit.