Strong-Coupling Diagram Technique for Strong Electron Correlations

Abstract

Using the strong coupling diagram technique a closed set of equations was derived for the electron Green’s function of the Hubbard model. Spectral functions calculated self-consistently in the two-dimensional t-U model are in qualitative and in some cases quantitative agreement with results of Monte Carlo simulations in a wide range of electron concentrations. For three different initial bands – the semi-elliptical density of states, t-U and t-t′-U models – the Mott transition occurs at very close values of the Hubbard repulsion $U_{c} \approx \sqrt{3}\varDelta /2$, where Δ is the initial bandwidth. The behavior of the Mott gap with doping and its width at half-filling depend strongly on the value of the next-nearest hopping constant t′.