Position space formulation for Dirac fermions on honeycomb lattice

We study how to construct Dirac fermion defined on the honeycomb lattice in position space. Starting from the nearest neighbor interaction in tight binding model, we show that the Hamiltonian is constructed by kinetic term and second derivative term of three flavor Dirac fermions in which one flavor has a mass of cutoff order and the other flavors are massless. In this formulation, the structure of the Dirac point is simplified so that its uniqueness can be easily shown even if we consider the next-to-nearest neighbor interaction. We also show that there is a hidden exact <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry (flavor–chiral symmetry) at finite lattice spacing, which protects the masslessness of the Dirac fermion, and discuss the analogy with the staggered fermion formulation