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arXiv · 2404.18441

Non-Hermitian Lattice Fermions in 2D GNY Model

Xingyu Guo·Chen-Te Ma·Hui Zhang
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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.

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Xingyu Guo, Chen-Te Ma, Hui Zhang. 2024-04-29. Non-Hermitian Lattice Fermions in 2D GNY Model. https://arxiv.org/abs/2404.18441

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