Creutz fermions on an orthogonal lattice

Abstract

In a recent paper, Creutz has given a new action describing two species of Dirac fermions with exact chiral symmetry on the lattice. This action depends on parameters which may be fixed at certain values in order to get the right continuum limit.In this letter, we elaborate more on this idea and present an action which is free of any other parameter except the fermion mass.

New chiral lattice actions of the Boriçi-Creutz type

“…where a is an orthogonal matrix [2]. The specific values of the entries of γ 0 μ depend on the actual location of the second zero.…”

“…Graphene-inspired Boriçi-Creutz fermions [1][2][3][4] sparked off a revival of minimally doubled actions a few years ago (a recent overview is in Ref. [5]).…”

Gross-Neveu model with Borici-Creutz fermion

“…The action was defined on a honeycomb or graphene lattice with tunable parameters to control the magnitude of p µ . Borici [4] immediately found a solution for the parameters such that the two flavors are located at the origin and at ( ). The chirally-invariant Borici-Creutz (BC) action breaks hypercubic and discrete symmetries such as parity and time-reversal and thus allows non-covriant counter terms through quantum corrections [5].…”

Lattice QCD with mixed action – Borici-Creutz valence quark on staggered sea

“…This can be helpful for N f = 2 lattice simulations, and is relatively simpler and possibly faster than Ginsparg-Wilson fermions. There are two main variants of the minimally doubled fermions -Karsten-Wilczek [1,2], Borici-Creutz [3,4]. In this work, we study mixed action lattice QCD with Borici-Cruetz valence quarks in Asqtad improved staggered sea, restricting to light quarks only.…”