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

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 N-c exists, below which chiral symmetry can be broken spontaneously. Values for N-c 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); D. 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 < N-c <2 [S. Hands, Phys. Rev. D 99, 034504 (2019)]. However, in the latter simulations difficulties in reaching the massless limit in the broken phase (at strong coupling and after the L-s -> infinity limit has been taken) are encountered. To find an accurate value N-c we study the Thirring model (by using an analytic continuation of the parity even theory to arbitrary real N) for N between 0.5 and 1.1. We investigate the chiral condensate, the spectral density of the Dirac operator, the spectrum of (would-be) Goldstone bosons and the variation of the filling-factor and conclude that the critical flavor number is N-c=0.80(4). Thus we see no chiral symmetry breaking in all Thirring models with 1 or more flavors of (4-component) fermions. Besides the transition to the unphysical lattice artifact phase we find strong evidence for a hitherto unknown phase transition that exists for N > N-c and should answer the question of where to construct a continuum limit.