Studies of Electronic Inhomogeneities in Strongly Correlated Systems Using Quantum Cluster Methods

In order to understand various local phenomena related to electronic phase separa-tion discovered recently in strongly correlated materials, quantum cluster methods are applied to a theoretical model, i.e., Hubbard model, which has successfully predicted basic properties of strongly correlated systems. Our calculations are performed at two levels: exact calculations based on the isolated small clusters via exact diagonalization and approximate calculations applied to large lattices using the variational cluster approximation (VCA). We first study phase separation instabilities with the formation of a pairing gap in the two-dimensional Hubbard model for 8-site Betts clusters. The exact diag-onalization method is applied to extract exact ground and excited states of the Hubbard model. The results show that the electronic states with one hole off half filling are unstable and they energetically prefer creating the spatial phase separation. The effect of next nearest hopping is also discussed in this part. We studied the variation of the pairing when the out-of-plane correlation is present by adding an interacting apical site above the two-dimensional cluster plane. Th