Lattice fermions as spectral graphs
arXiv:2112.13501 · doi:10.1007/JHEP02(2022)104
Abstract
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac operators even on the non-torus and non-regular lattice, leading to understanding of the number of fermion species (doublers) on lattices with arbitrary topologies. The procedure of application of SGT to lattice fermions is summarized as follows: (1) One investigates a spectral graph corresponding to a lattice fermion. (2) One obtains a matrix corresponding to the graph. (3) One finds zero eigenvalues of the matrix by use of the discrete Fourier transformation (DFT). (4) By taking an infinite-volume and continuum limits, one finds the number of species. We apply this procedure to the known lattice fermion formulations including Naive fermions, Wilson fermions and Domain-wall fermions, and reproduce the known fact on the number of species. We also apply it to the lattice fermion on the discretized four-dimensional hyperball and discuss the number of fermion species on the bulk. In the end of the paper, we discuss the application of the analysis to lattice fermions on generic lattices with arbitrary topologies, which could lead to constructing a new theorem regarding the number of species.
arXiv comment29 pages, 11 figures
References in corpus (43)
- A Method for Simulating Chiral Fermions on the Lattice
- Chiral Fermions from Lattice Boundaries
- More about exactly massless quarks on the lattice
- Axial symmetries in lattice QCD with Kaplan fermions
- Four-dimensional graphene and chiral fermions
- Creutz Fermions on an Orthogonal Lattice
- Broken Symmetries from Minimally Doubled Fermions
- The Scaling of Exact and Approximate Ginsparg-Wilson Fermions
- Renormalization of minimally doubled fermions
- Theoretical foundation for the Index Theorem on the lattice with staggered fermions
- Meson and Baryon dispersion relations with Brillouin fermions
- Single flavor staggered fermions
- Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
- Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
- Minimally doubled fermions at one loop
- Search for Fermion Actions on Hyperdiamond Lattices
- Pairs of chiral quarks on the lattice from staggered fermions
- Classification of Minimally Doubled Fermions
- Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices
- Brillouin improvement for Wilson fermions
- Anomalies and symmetric mass generation for Kaehler-Dirac fermions
- Taste-split staggered actions: eigenvalues, chiralities and Symanzik improvement
- Revisiting symmetries of lattice fermions via spin-flavor representation
- Phase structure for lattice fermions with flavored chemical potential terms
- Improved lattice fermion action for heavy quarks
- Chiral Lattice Fermions, Minimal Doubling, and the Axial Anomaly
- Numerical properties of staggered quarks with a taste-dependent mass term
- Topological fermion condensates from anomalies
- Characters of Lattice Fermions Based on the Hyperdiamond Lattice
- QCD phase diagram with 2-flavor lattice fermion formulations
- Reducing the number of counterterms with new minimally doubled actions
- Dispersion relation and spectral range of Karsten-Wilczek and Borici-Creutz fermions
- Varieties and properties of central-branch Wilson fermions
- Fermion Actions extracted from Lattice Super Yang-Mills Theories
- Strong-coupling Analysis of Parity Phase Structure in Staggered-Wilson Fermions
- Minimal Doubling Fermion and Hermiticity
- Many avatars of the Wilson fermion: A perturbative analysis
- New chiral lattice actions of the Borici-Creutz type
- Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model
- On the suitability of the Brillouin action as a kernel to the overlap procedure
- The Volume of the Quiver Vortex Moduli Space
- Supersymmetric Gauge Theory on the Graph
- Numerical properties of staggered overlap fermions