  By combining the tetrahedron method with the cluster perturbation theory
(CPT), we present an accurate method to numerically calculate the density of
states of interacting fermions without introducing the Lorentzian broadening
parameter $\eta$ or the numerical extrapolation of $\eta \to 0$. The method is
conceptually based on the notion of the effective single-particle Hamiltonian
which can be subtracted in the Lehmann representation of the single-particle
Green's function within the CPT. Indeed, we show the general correspondence
between the self-energy and the effective single-particle Hamiltonian which
describes exactly the single-particle excitation energies of interacting
fermions. The detailed formalism is provided for two-dimensional multi-orbital
systems and a benchmark calculation is performed for the two-dimensional
single-band Hubbard model. The method can be adapted straightforwardly to
symmetry broken states, three-dimensional systems, and finite-temperature
calculations.
