  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
$\langle\phi\rangle$, $\langle\phi^2\rangle$,
$\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)/2\rangle$, and
$\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)\phi/2\rangle$. We
also used the one-loop resummation to provide the RG flow and asymptotic safety
in the 2D GNY model.
