We define a sparse hermitian lattice Dirac matrix, H, coupling 2n+ 1 Dirac fermions. When 2n fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of H and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusi...

Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input-output finite-dimensional portHamiltonian systems that...

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.

A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge con...

In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are presented. The theory is illustrated on the example of the ideal transmission line. keywords: Power conserving structures, Dirac structures, Representations. AMS-Classification: 93C25, 93A30, 93B10, 70...

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configur...

The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is ...

Spin-polarized gapless surface states in topological insulators form chiral Dirac cones. When such materials are reduced to thin films, the Dirac states on the two faces of the film can overlap and couple by quantum tunneling, resulting in a thickness-dependent insulating gap at the Dirac point. Calculations for a freestanding Sb film with a thickness of four atomic bilayers yield a gap of 36 m...

We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenvalue of the Dirac operator for non-trivial spin structures. It is the only explicit estimate for eigenvalues of the Dirac operator known so far that uses information about the spin structure. As a corollary we obtain lo...

We formulate Dirac-Kähler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kähler action requires to choose the lattice structure having both orientabilities on a link. The Kogut-Susskind fermion and the staggered fermion actions are derived directly from the Dirac-Kähler fermion formulated by the Clifford product....