Influence of finite chemical potential on the fermion chiral condensate in QED3

Abstract In this Letter, we generalize our previous work [H.T. Feng, F.Y. Hou, X. He, W.M. Sun, H.S. Zong, Phys. Rev. D 73 (2006) 016004] on the effect of finite chemical potential μ on the fermion propagator in QED 3 from the rainbow approximation (bare vertex approximation) of the Dyson–Schwinger approach to the case of an improved fermion–photon vertex ansatz. We show that, for this choice of the fermion–photon vertex the fermion propagator at finite chemical potential can still be written as S ˆ −1 ( μ , p ) = i γ ⋅ p ˜ A ( p ˜ 2 ) + B ( p ˜ 2 ) , where p ˜ = ( p → , p 3 + i μ ) and S −1 ( p ) = i γ ⋅ p A ( p 2 ) + B ( p 2 ) is the fermion propagator at μ = 0 . By application of this result, the fermion chiral condensate is evaluated for the range N ∈ [ 0 , 3.0 ] ( N denotes the number of fermion flavors) and μ ∈ [ 0 , 10 −2 ] and the influence of small chemical potential on the critical number of fermion flavors N c is analyzed. A comparison with the rainbow approximation results is made.