48 research outputs found
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-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.Comment: 19 pages, 7 figure
Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours
We present details of a lattice study of infrared behaviour in SU(3) gauge
theory with twelve massless fermions in the fundamental representation. Using
the step-scaling method, we compute the coupling constant in this theory over a
large range of scale. The renormalisation scheme in this work is defined by the
ratio of Polyakov loops in the directions with different boundary conditions.
We closely examine systematic effects, and find that they are dominated by
errors arising from the continuum extrapolation. Our investigation suggests
that SU(3) gauge theory with twelve flavours contains an infrared fixed point.Comment: 29 pages, 15 figures, 4 tables. Minor revision. Published versio