Momentum dependence of quantum critical Dirac systems
Lennart Dabelow (Fakultät für Physik, Universität Bielefeld, 33615 Bielefeld, Germany); Holger Gies (Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany and Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena, Germany); Benjamin Knorr (Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands)
We analyze fermionic criticality in relativistic dimensional fermion systems using the functional renormalization group (FRG), concentrating on the Gross-Neveu (chiral Ising) and the Thirring model. While a variety of methods, including the FRG, appear to reach quantitative consensus for the critical regime of the Gross-Neveu model, the situation seems more diverse for the Thirring model with different methods yielding vastly different results. We present a first exploratory FRG study of such fermion systems including momentum-dependent couplings using pseudo-spectral methods. Our results corroborate the stability of results in Gross-Neveu-type universality classes, but indicate that momentum dependencies become more important in Thirring-type models for small flavor numbers. For larger flavor numbers, we confirm the existence of a non-Gaussian fixed point and thus a physical continuum limit. In the large- limit, we obtain an analytic solution for the momentum dependence of the fixed-point vertex.