The Staggered Fermion for the Gross-Neveu Model at Non-zero Temperature and Density

The 2+1d Gross-Neveu model with finite density and finite temperature are studied by the staggered fermion discretization. The kinetic part of this staggered fermion in momentum space is used to build the relation between the staggered fermion and Wilson-like fermion. In the large Nf limit (the number Nf of staggered fermion flavors), the chiral condensate and fermion density are solved from the gap equation in momentum space, and thus the phase diagram of fermion coupling, temperature and chemical potential are obtained. Moreover, an analytic formula for the inverse of the staggered fermion matrix are given explicitly, which can be calculated easily by parallelization. The generalization to the 1+1d and 3+1d cases are also considered.