| The strongly correlated electron system such as the high {dollar}Tsb{lcub}c{rcub}{dollar} superconductor and the organic conductor are studied with the tight-binding model and the Hubbard model. Continuum approximations of the electronic structure of the spherical molecules such as fullerenes and small artificial clusters are presented with the tight-binding model. For these molecules, instability is found for the ferromagnetic state of two-holes doped at half-filling with the infinite repulsion Hubbard model. As the prototype of the strongly correlated electron system, the Hubbard model may be related to the non-Fermi liquid behavior of materials such as high {dollar}Tsb{lcub}c{rcub}{dollar} superconductor. Unlike the one-dimensional case, there is a limitation of the Bethe ansatz approach for higher dimensions. We discuss the difficulties of the Bethe ansatz method for the two-dimensional Hubbard model. Using the density-matrix renomalization-group method and the recursion technique we are able to study the two-chain Hubbard model along with the one-chain Hubbard model. We calculate the dynamical correlation functions such as the excitation spectra of charge and spin and check the differences of the dynamics of charge and spin for both one-chain and two-chain Hubbard model. We derive the phase diagram of the two-chain Hubbard model by the calculations of four gaps for charge and spin, symmetric and antisymmetric modes with respect to the exchange of the chain indices, respectively. We see the difference between the weak interaction case and the strong interaction case. |
