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arXiv · 1903.07388

Momentum dependence of quantum critical Dirac systems

Lennart Dabelow·Holger Gies·Benjamin Knorr
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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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Lennart Dabelow, Holger Gies, Benjamin Knorr. 2019-03-18. Momentum dependence of quantum critical Dirac systems. https://doi.org/10.1103/physrevd.99.125019

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