Non-Hermitian Lattice Fermions in 2D GNY Model

We work the lattice fermions and non-Hermitian formulation in the 2D 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 non-symmetrized 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 $\langleφ\rangle$, $\langleφ^2\rangle$, $\langle\mathrm{Tr}(\barψ_1ψ_1+\barψ_2ψ_2)/2\rangle$, and $\langle\mathrm{Tr}(\barψ_1ψ_1+\barψ_2ψ_2)φ/2\rangle$. We also used the one-loop resummation to provide the RG flow and asymptotic safety in the 2D GNY model.