Non-Hermitian lattice fermions in the 2D Gross-Neveu-Yukawa model

We work the lattice fermions and non-Hermitian formulation in the 2D Gross-Neveu-Yukawa (GNY) model and demonstrate the numerical implementation for two flavors by the hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the nonsymmetrized finite-difference operator. We restore the hypercubic symmetry by averaging over all possible orientations with the proper continuum limit. Our study is the first simulation for the interacting fermion formulated in a non-Hermitian way. We compare the numerical solution with the one-loop resummation. The resummation results matches with the numerical solution in ⟨ϕ⟩, ⟨ϕ2⟩, ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)/2⟩, and ⟨Tr(ψ¯1ψ1+ψ¯2ψ2)ϕ/2⟩. We also used the one-loop resummation to provide the renormalization group flow and asymptotic safety in the 2D GNY model. Published by the American Physical Society 2024