Related papers: Position space formulation for Dirac fermions on h…
We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around…
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we…
In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the…
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands…
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great…
A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces…
We consider the fate of the Dirac points in the spectrum of a honeycomb optical lattice in the presence of a harmonic confining potential. By numerically solving the tight binding model we calculate the density of states, and find that the…
In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. We construct…
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each link. Care is taken so the construction…
According to the necessary requirements for a chirally symmetric Dirac operator, we present a systematic construction of such operators. We formulate a criterion for the hermitian operator which enters the construction such that the doubled…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice while preserving unitarity and locality and without breaking the chiral symmetry. The fermion doubling problem is circumvented by constructing a…
In paper within the model with a maximal mass M and with use of anti de Sitter space is considered the Dirac equation properties for a fermion of mass m on the mass surface. The paper shows that free Hamiltonian and Hamiltonian with…
Silicene, a sheet of silicon atoms in a honeycomb lattice, was proposed to be a new Dirac-type electron system similar as graphene. We performed scanning tunneling microscopy and spectroscopy studies on the atomic and electronic properties…
We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the…
Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results of the usual…
We construct a solution to the equation of motion of Hamiltonian lattice QCD in the strong coupling limit using Wilson fermions which exactly diagonalizes the Hamiltonian to second order in the field operators. This solution obeys the free…
The Dirac fermion with linear dispersion in the kagom\'e lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry…
We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic…
We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or…