Non local theory of excitations applied to the Hubbard model

TL;DR

This paper introduces a nonlocal theoretical approach for analyzing single-particle excitations in the Hubbard model, capturing long-range correlations and strong interaction effects with high momentum resolution.

Contribution

It develops a nonlocal effective medium theory using the projection operator method, improving upon single-site approximations for strongly correlated systems.

Findings

Reproduces sub-bands due to antiferromagnetic correlations in strong Coulomb regimes.

Shows reduction of quasi-particle peak with increasing Coulomb interaction.

Shifts critical Coulomb interaction Uc2 for effective mass divergence higher than single-site results.

Abstract

We propose a nonlocal theory of single-particle excitations. It is based on an off-diagonal effective medium and the projection operator method for treating the retarded Green function. The theory determines the nonlocal effective medium matrix elements by requiring that they are consistent with those of the self-energy of the Green function. This arrows for a description of long-range intersite correlations with high resolution in momentum space. Numerical study for the half-filled Hubbard model on the simple cubic lattice demonstrates that the theory is applicable to the strong correlation regime as well as the intermediate regime of Coulomb interaction strength. Furthermore the results show that nonlocal excitations cause sub-bands in the strong Coulomb interaction regime due to strong antiferromagnetic correlations, decrease the quasi-particle peak on the Fermi level with increasing Coulomb interaction, and shift the critical Coulomb interaction Uc2 for the divergence of effective mass towards higher energies at least by a factor of two as compared with that in the single-site approximation.