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Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling
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I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. Outlook
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Lattice Chiral Fermion without Hermiticity
A review of lattice fermion formulations, centered on a non-Hermitian one-sided-difference approach that avoids doublers while preserving chiral symmetry, plus surveys of Wilson, overlap, topological charge, and Monte...
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