Spontaneous symmetry breaking of SO(2N) in Gross-Neveu theory from 2+ε expansion
- Stamou
Abstract:
It was recently established that the paradigmatic Gross--Neveu model with N copies of two-dimensional Dirac fermions features an SO(2N) symmetry if certain interactions are suppressed. This becomes evident when the theory is rewritten in terms of 2N copies of two-dimensional Majorana fermions. Mean-field theory for the SO(2N) model predicts, besides the chiral Ising transition at gc1, a second critical point gc2 where SO(2N) is broken down to SO(N)×SO(N). A subsequent Wilsonian renormalization group analysis directly in d=3 supports its existence in a generalized theory, where Nf copies of the 4N-component Majorana fermions are introduced. This allows to track the evolution of a (i) quantum anomalous Hall Gross--Neveu--Ising, (ii) symmetric-tensor, and (iii) adjoint-nematic fixed point separately. However, it turns out that (ii) and (iii) lose their criticality when approaching Nf=1, suggesting that the transition is first order. In this work, we approach the problem from the lower-critical dimension of two. We construct a Fierz-complete renormalizable Lagrangian, compute the leading order β functions, fermion anomalous dimension, as well as the order parameter anomalous dimensions, and resolve the three universality classes corresponding to (i)--(iii). Before becoming equal to the Gaussian fixed point at Nf=1, (ii) remains critical for all values of Nf>NSTf,c(N)≈0.56+1.48N+(ϵ), which compares well with the estimate of previous studies. We further find that (iii) becomes equal to (i) when approaching Nf=1. An instability is, however, only present in the susceptibility corresponding to the Gross--Neveu--Ising order parameter.
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