Density of states at different interaction strengths with (a) T=0.05, t 2 = 0 , (b) T=0.05, t 2 = 0.2 , (c) T=0.05, t 2 = 0.5 , and (d) T=0.1, t 2 = 0.5 . The frequency ω (which is also the energy, because we set the reduced Planck constant to unity) is counted from the chemical potential.