A Study Of Fermion Bag Approach On Gross-Neveu Model

In this paper,we study the 2+1d Gross-Neveu(GN)model with non-zero temperature and finite density.The 2+1d GN model in Euclidean space is introduced both in a continuous form and with the discretization scheme of the staggered fermion.We use the fermion bag approach to caculate the fermion density and chiral condensate of the 2+1d GN model.The dependence of these two thermodynamic quantities on the chemical potential?,the flavor number N_f,coupling strength g and mass m are studied and the numerical results are compared with those of the complex Langevin dynamics.The complex Langevin dynamics needs to solve the inverse of the fermion matrix,whose computation is proportional to the third power of the order of the matrix,so the efficiency is very low.The fermion bag approach applys the determinant algorithm and thus reduces the computation cost.It is found that more difficulties are encountered in solving the inverse of fermion matrix as m is reduced.As a result,the computational efficiency for the complex Langevin dynamics becomes worse.The fermion bag approach has a high computational efficiency for the strong interaction between fermions.It is shown that the flavor number N_fhas little influence on the fermion density and chiral condensate.While the coupling strength g becomes larger,the fermion density becomes smaller and the chiral condensate decreases faster as the chemical potential is increasing.While the mass m becomes smaller,the fermion density becomes larger and converges to the same curve slowly.When m is near 0,the chiral condensate decreases rapidly with increasing chemical potential.The results of the fermion bag approach are a little bit different from those of the complex Langevin dynamics.The fermion density is a little larger and the chiral condensate is a little smaller in the fermion bag approach.