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

TL;DR

This paper introduces a precise numerical method combining the tetrahedron scheme with cluster perturbation theory to calculate the density of states for interacting fermions without broadening parameters or extrapolation.

Contribution

The paper develops a novel approach integrating the tetrahedron method with CPT, enabling accurate density of states calculations for interacting fermions without Lorentzian broadening.

Findings

Accurate density of states calculation without broadening parameter.

General formalism applicable to multi-orbital and 3D systems.

Benchmark validation on the 2D Hubbard model.

Abstract

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.