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Momentum dependence of quantum critical Dirac systems

Lennart Dabelow*

Holger Gies†

Benjamin Knorr‡

  • Fakultät für Physik, Universität Bielefeld, 33615 Bielefeld, Germany

  • 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

  • Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands

  • *ldabelow@physik.uni-bielefeld.de
  • †holger.gies@uni-jena.de
  • ‡b.knorr@science.ru.nl
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Phys. Rev. D 99, 125019 – Published 28 June, 2019

DOI: https://doi.org/10.1103/PhysRevD.99.125019

Abstract

We analyze fermionic criticality in relativistic 2+1 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-N limit, we obtain an analytic solution for the momentum dependence of the fixed-point vertex.

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Phys. Rev. D 99, 125019– Published 28 June, 2019
  • Received 23 May 2019
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