We may then construct many-body hybridization function between the system excited states and the bath (which is analogous to the single-orbital hybridization in Eq. 35): We investigate four different Γs: 10 -2 , 10 -3 , 10 -4 , 10 -5 . Note that both Γ1 and Γ2 have a dip at the symmetric point, where the onsite energy ϵ d (x) reaches the fermi level ϵ f = 0. We calculate Γ1 and Γ2 using a lorentzian function to approximate the delta function in Eq. 63: i.e. δ(x -x 0 ) ≈