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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">⟨</a:mo><a:mi>ϕ</a:mi><a:mo stretchy="false">⟩</a:mo></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mo stretchy="false">⟨</e:mo><e:msup><e:mrow><e:mi>ϕ</e:mi></e:mrow><e:mrow><e:mn>2</e:mn></e:mrow></e:msup><e:mo stretchy="false">⟩</e:mo></e:mrow></e:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mo stretchy="false">⟨</i:mo><i:mi>Tr</i:mi><i:mo stretchy="false">(</i:mo><i:msub><i:mrow><i:mover accent="true"><i:mrow><i:mi>ψ</i:mi></i:mrow><i:mrow><i:mo stretchy="false">¯</i:mo></i:mrow></i:mover></i:mrow><i:mrow><i:mn>1</i:mn></i:mrow></i:msub><i:msub><i:mrow><i:mi>ψ</i:mi></i:mrow><i:mrow><i:mn>1</i:mn></i:mrow></i:msub><i:mo>+</i:mo><i:msub><i:mrow><i:mover accent="true"><i:mrow><i:mi>ψ</i:mi></i:mrow><i:mrow><i:mo stretchy="false">¯</i:mo></i:mrow></i:mover></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msub><i:msub><i:mrow><i:mi>ψ</i:mi></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msub><i:mo stretchy="false">)</i:mo><i:mo>/</i:mo><i:mn>2</i:mn><i:mo stretchy="false">⟩</i:mo></i:mrow></i:math>, and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mo stretchy="false">⟨</s:mo><s:mi>Tr</s:mi><s:mo stretchy="false">(</s:mo><s:msub><s:mrow><s:mover accent="true"><s:mrow><s:mi>ψ</s:mi></s:mrow><s:mrow><s:mo stretchy="false">¯</s:mo></s:mrow></s:mover></s:mrow><s:mrow><s:mn>1</s:mn></s:mrow></s:msub><s:msub><s:mrow><s:mi>ψ</s:mi></s:mrow><s:mrow><s:mn>1</s:mn></s:mrow></s:msub><s:mo>+</s:mo><s:msub><s:mrow><s:mover accent="true"><s:mrow><s:mi>ψ</s:mi></s:mrow><s:mrow><s:mo stretchy="false">¯</s:mo></s:mrow></s:mover></s:mrow><s:mrow><s:mn>2</s:mn></s:mrow></s:msub><s:msub><s:mrow><s:mi>ψ</s:mi></s:mrow><s:mrow><s:mn>2</s:mn></s:mrow></s:msub><s:mo stretchy="false">)</s:mo><s:mi>ϕ</s:mi><s:mo>/</s:mo><s:mn>2</s:mn><s:mo stretchy="false">⟩</s:mo></s:mrow></s:math>. 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