Renormalized Mean Field Study Of Strongly Correlated Systems

This thesis starts from a brief review of current progress in the study of strongly correlated systems. After an introduction for the mean field theory I present our studies on three relevant topics:charge ordered resonating-valence-bond(RVB) state in the doped cuprates, renormalized mean field approach to two-dimensional checkerboard lattice as well as that to three dimensional sys-tems.By using renormalized mean field theory we study charge ordered d-wave resonating valence bond states (dRVB) in doped cuprates, and estimate their energies in the t - J model. The long-range Coulomb potential tends to mod-ulate the charge density in favor of the charge-ordered RVB state while the kinetic energy Ht prefers a uniform charge distribution. The balance of these two effects may result in stable charge ordered patterns. The possible rele-vance to the observed 4×4 checkerboard patterns in tunnelling conductance in high Tc cuprates is discussed.We study the t-t'-J-J'model on two-dimensional bipartite checkerboard lattices by considering uniform electric charge concentration. We define a parameter a to be the ratio between the couplings along the diagonal directions (denoted by a, b) and that along x-and y-axes. Our results illustrate that systems with distinct a show different properties. Namely for│α│=1, at half filling the ground state has a symmetry of d+id. Inα=1 case,△a,b drop rapidly in the presence of doping. When concentration reachesδ=0.02,△a,b=0 and the system behavior just like a square lattice. Forα=-1 case, d-wave symmetry of△a,b and△x,y persist in the presence of doping. For thisα=-1 case with doping larger than 0.05 there exist a novel solution with exactly s-wave symmetry of△a,b(△a=△b). This solution has a tinily lower energy than that of d+id state.Additionally, we extend the variational method for t-J model on two-dimensional square lattice to three-dimensional simple cubic (SC) and face centered cubic (FCC) lattices, respectively. We find that there are 27r/3-phase differences between the pairing order parameters along the three orthogonal directions for SC lattice. A distinct two-dimensional behavior emerges rapidly when the coupling constant in a certain direction diminishes. Whereas, for FCC lattice, there are three different solutions for half-filled case, while there are four solutions with different symmetries in the presence of doping. The one with d-wave order△in one plane have lower energy in low doping case, while in high doping density case those solutions have same energies.