Position space formulation for Dirac fermions on honeycomb lattice

TL;DR

This paper develops a position space formulation for Dirac fermions on the honeycomb lattice, clarifying the Dirac point structure, chiral symmetry, and mass protection mechanisms, even with next-nearest neighbor interactions.

Contribution

It introduces a position space approach for Dirac fermions on the honeycomb lattice, simplifying the Dirac point structure and analyzing chiral symmetry at finite lattice spacing.

Findings

Hamiltonian constructed from kinetic and second derivative terms of three flavor Dirac fermions

Dirac point structure is simplified and shown to be unique even with next-nearest neighbor interactions

Chiral symmetry at finite lattice spacing protects fermion masslessness

Abstract

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-nearest neighbor interaction. We also show the chiral symmetry at finite lattice spacing, which protects the masslessness of the Dirac fermion, and discuss the analogy with the staggered fermion formulation.