Evolution of the spectrum of the Hubbard model with filling

TL;DR

This paper develops a diagrammatic technique for the Hubbard model at moderate to strong repulsion, revealing how the electronic spectrum evolves with filling, including the emergence of a narrow band near the Fermi level.

Contribution

It formulates a new diagrammatic approach using site cumulants for the Hubbard model and analyzes the spectral evolution with electron filling, including the appearance of a narrow band.

Findings

A new narrow band appears near the Fermi level at low fillings.

The dispersion and bandwidth of the new band resemble the spin-polaron band in the t-J model.

The method provides insights into the spectral evolution with electron concentration.

Abstract

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions and nearest-neighbor hopping. With decreasing the electron concentration in addition to the four bands observed at half-filling a narrow band arises near the Fermi level. The dispersion of the new band, its bandwidth and the variation with filling are close to those of the spin-polaron band in the t-J model.