Non-Hermitian Lattice Fermions in 2D GNY Model

TL;DR

This paper introduces a novel non-Hermitian lattice fermion formulation for the 2D GNY model, enabling efficient numerical simulations that preserve chiral symmetry and match analytical resummation results, advancing understanding of RG flow and asymptotic safety.

Contribution

It presents the first simulation of interacting fermions in a non-Hermitian framework, avoiding the Nielsen-Ninomiya theorem and restoring symmetry through averaging, with validation against one-loop resummation.

Findings

Numerical results agree with one-loop resummation for key observables.

The approach preserves chiral symmetry without fermion doubling.

Provides insights into RG flow and asymptotic safety in 2D GNY model.

Abstract

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.