Local moment approach to multi-orbital Anderson and Hubbard models

The variational local moment approach (V-LMA), being a modification of the method due to Logan {\it et al}., is presented here. The existence of local moments is taken from the outset and their values are determined through variational principle by minimizing the corresponding ground state energy. Our variational procedure allows us to treat both fermi- and non-fermi liquid systems with many orbitals as well as insulators without any additional assumptions. It is proved by an explicit construction of the corresponding Ward functional that the V-LMA belongs to the class of conserving approximations. As an illustration, the V-LMA is used to solve the multi-orbital single impurity Anderson model. The method is also applied to solve the dynamical mean-field equations for the multi-orbital Hubbard model. In particular, the Mott-Hubbard metal--insulator transition is addressed within this approach.