Full Self-Consistent Projection Operator Approach to Nonlocal Excitations in Solids

TL;DR

This paper introduces a self-consistent projection operator method that accurately captures nonlocal excitations and long-range correlations in solids, providing high-resolution momentum-dependent spectra applicable across various interaction strengths.

Contribution

It develops a novel self-consistent approach incorporating long-range correlations via an incremental cluster expansion, advancing the understanding of nonlocal excitations in solid-state systems.

Findings

The method accurately describes momentum-dependent excitation spectra.

Long-range antiferromagnetic correlations cause shadow bands and sub-peaks.

Applicable across a wide range of Coulomb interaction strengths.

Abstract

A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott-Hubbard bands.