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 Uc ≈ √3 Δ/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'.