Abstract
The 2 + 1d Gross-Neveu model with finite density and finite temperature is 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 is obtained. Moreover, an analytic formula for the inverse of the staggered fermion matrix is given explicitly, which can be calculated easily by parallelization. The generalization to the 1 + 1d and 3 + 1d cases is also considered.
Highlights
Since the chiral symmetry breaking and restoration are intrinsically nonperturbative, the number of techniques is limited and most results come from the lattice quantum chromodynamics (QCD)
In the large N f limit, the chiral condensate and fermion density are solved from the gap equation in momentum space, and the phase diagram of fermion coupling, temperature and chemical potential is obtained
The tensor network becomes very popular in condensed matter physics and high energy physics, especial for lower dimension models, since probability is not used and it is free of sign problem [12] [13] [14] [15]
Summary
Since the chiral symmetry breaking and restoration are intrinsically nonperturbative, the number of techniques is limited and most results come from the lattice QCD. This paper addresses a simplest four-fermion model with Z2 symmetry: Gross-Neveu model at non-zero temperature and density [16] [17] [18] [19] [20]. The 2 + 1d Gross-Neveu model has an interesting continuum limit and there is a critical coupling indicating the threshold for the symmetry breaking at zero temperature and density. Compared with the Wilson fermion, the staggered fermion is more adequate for studying spontaneous chiral symmetry breaking. We revisit the staggered fermion for the 1 + 1d, 2 + 1d and 3 + 1d Gross-Neveu model at non-zero temperature and finite density.
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