Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms

Abstract

We investigate the parity-broken phase structure for staggered and naive fermions in the Gross-Neveu model as a toy model of QCD. We consider a generalized staggered Gross-Neveu model including two types of four-point interactions. We use generalized mass terms to split the doublers for both staggered and naive fermions. The phase boundaries derived from the gap equations show that the mass splitting of tastes results in an Aoki phase both in the staggered and naive cases. We also discuss the continuum limit of these models and explore taking the chirally-symmetric limit by fine-tuning a mass parameter and two coupling constants. This supports the idea that in lattice QCD we can derive one- or two-flavor staggered fermions by tuning the mass parameter, which are likely to be less expensive than Wilson fermions in QCD simulation.

arXiv comment31 pages, 14 figures; typos corrected

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• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_1$--$J_2$ model
• Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
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• Taste-split staggered actions: eigenvalues, chiralities and Symanzik improvement
• Lattice-fermionic Casimir effect and topological insulators
• Phase structure for lattice fermions with flavored chemical potential terms
• Quantum phases of hard-core bosons in a frustrated honeycomb lattice
• Lattice gauge theory for Haldane conjecture and central-branch Wilson fermion
• Reducing the number of counterterms with new minimally doubled actions
• Higher order topological matter and fractional chiral states
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• Varieties and properties of central-branch Wilson fermions
• Kondo effect with Wilson fermions
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• Four Fermion Interactions in Non-Abelian Gauge Theory
• Many avatars of the Wilson fermion: A perturbative analysis
• Generative learning for the problem of critical slowing down in lattice Gross Neveu model
• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Lattice fermions as spectral graphs
• Gross-Neveu model with Borici-Creutz fermion
• Broken discrete and continuous symmetries in two dimensional spiral antiferromagnets
• On Flavor Symmetry in Lattice Quantum Chromodynamics
• Mass spectroscopy using Borici-Creutz fermion on 2D lattice
• Equivalence of lattice operators and graph matrices
• Spin-taste representation of minimally doubled fermions from first principles: Karsten-Wilczek fermions
• New fermion discretizations and their applications
• Aoki Phases in Staggered-Wilson Fermions
• Minimal-doubling and single-Weyl Hamiltonians
• Non-${\gamma }_5$hermiticity fermions in two dimensions
• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
• Twisted 3D $N=4$ Supersymmetric YM on deformed ${\mathbb{A}}_3^{\ast }$ Lattice
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group