Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

Abstract

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form $\mathcal{H}\psi =E\mathcal{P}\psi$, with Hermitian tight-binding operators $\mathcal{H}$, $\mathcal{P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

arXiv comment16 pages, 3 figures

References in corpus (23)

• Topological Insulators
• Topological insulators and superconductors
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Anderson Transitions
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Finite difference method for transport properties of massless Dirac fermions
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D
• The supersymmetric technique for random-matrix ensembles with zero eigenvalues
• Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Two-Dimensional Lattice Model for the Surface States of Topological Insulators
• Eigenvalue spectrum of massless Dirac operators on the lattice
• Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
• Single-cone real-space finite difference scheme for the time-dependent Dirac equation
• Staggered grid leap-frog scheme for the (2+1)D Dirac equation
• Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry
• Confinement and Fermion Doubling Problem in Dirac-like Hamiltonians
• Dynamics of domain-wall Dirac fermions on a topological insulator: a chiral fermion beam splitter
• Dirac Spectra of 2-dimensional QCD-like theories
• Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians

Cited by in corpus (13)

• Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling
• Majorana bound states in encapsulated bilayer graphene
• Topologically protected Casimir effect for lattice fermions
• Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone
• Helical Luttinger liquid on a space-time lattice
• Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Geometry-independent tight-binding method for massless Dirac fermions in two dimensions
• Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
• Boundary-induced Majorana coupling in a planar topological Josephson junction
• Single-cone Dirac edge states on a lattice
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice