| An improved two-pole approximation (ITPA) is proposed for the Anderson-Hubbard Model (AHM), which is a standard model to study disordered systems with strongly correlated electrons. Transition-metal oxides are a prominent example of such systems, and they are of interest since they exhibit very rich physics such as high-temperature superconductivity and giant magneto-resistance. There is no analytical solution to two and three dimensional AHM, and exact numerical solutions are very limited in system size. Therefore, several approximation schemes have been developed to study the AHM. Here, another approximation method is proposed, namely the ITPA, which is based on Mori-Zwanzig's projection operator, or Liouvillean superoperator, approach. It has two important aspects. First, the ITPA is a promising scheme since it successfully reproduces the exact numerical results for small systems, and is superior to similar approaches. Second, the ITPA differs from similar approaches since it includes some non-local correlations, which are of big importance in low dimensions. Thus the ITP approximation will give a more realistic phase diagram for the disordered and strongly correlated systems.; Keywords. the Anderson-Hubbard model, the disordered Hubbard model, disorder, strongly correlated electrons, two-pole approximation. |
