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By combining the tetrahedron method with the cluster perturbation theory(CPT), we present an accurate method to numerically calculate the density ofstates of interacting fermions without introducing the Lorentzian broadeningparameter $\eta$ or the numerical extrapolation of $\eta \to 0$. The method isconceptually based on the notion of the effective single-particle Hamiltonianwhich can be subtracted in the Lehmann representation of the single-particleGreen's function within the CPT. Indeed, we show the general correspondencebetween the self-energy and the effective single-particle Hamiltonian whichdescribes exactly the single-particle excitation energies of interactingfermions. The detailed formalism is provided for two-dimensional multi-orbitalsystems and a benchmark calculation is performed for the two-dimensionalsingle-band Hubbard model. The method can be adapted straightforwardly tosymmetry broken states, three-dimensional systems, and finite-temperaturecalculations.

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory